메뉴 건너뛰기




Volumn 34, Issue 4, 1997, Pages 339-403

The symmetries of solitons

Author keywords

Hidden symmetry; Integrable systems; Inverse scattering transform; Korteweg de vries equation; Lax pair; Loop group; Nonlinear schr dinger equation; Solitons

Indexed keywords


EID: 0031499613     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0273-0979-97-00732-5     Document Type: Article
Times cited : (83)

References (145)
  • 2
    • 0038910943 scopus 로고    scopus 로고
    • Ablowitz, M.J., Clarkson, P.A., Solitons, non-linear evolution equations and inverse scattering, Cambridge Univ. Press, 1991. MR 93g:35108
    • MR , vol.93 G , pp. 35108
  • 4
    • 4243485401 scopus 로고    scopus 로고
    • Ablowitz, M.J., Kaup, D.J., Newell, A.C. and Segur, H., Method for solving the Sine-Gordon equation, Phys. Rev. Lett. 30 (1973), 1262-1264. MR 53:9967
    • MR , vol.53 , pp. 9967
  • 5
    • 0016369301 scopus 로고    scopus 로고
    • The inverse scattering transform - Fourier analysis for nonlinear problems
    • Ablowitz, M.J., Kaup, D.J., Newell, A.C. and Segur, H., The inverse scattering transform - Fourier analysis for nonlinear problems, Stud. Appl. Math. 53 (1974), 249-315. MR 56:9108
    • (1974) Stud. Appl. Math. , vol.53 , pp. 249-315
    • Ablowitz, M.J.1    Kaup, D.J.2    Newell, A.C.3    Segur, H.4
  • 6
    • 0016369301 scopus 로고    scopus 로고
    • Ablowitz, M.J., Kaup, D.J., Newell, A.C. and Segur, H., The inverse scattering transform - Fourier analysis for nonlinear problems, Stud. Appl. Math. 53 (1974), 249-315. MR 56:9108
    • MR , vol.56 , pp. 9108
  • 8
    • 0039503569 scopus 로고    scopus 로고
    • Abraham, R., Marsden, J.E., Foundations of Mechanics, Benjamin/Cummings, 1978. MR 81e:58025
    • MR , vol.81 E , pp. 58025
  • 9
    • 34250286595 scopus 로고    scopus 로고
    • On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-de Vries equation
    • Adler, M., On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-de Vries equation, Invent. Math 50 (1979), 219-248. MR 80i:58026
    • (1979) Invent. Math , vol.50 , pp. 219-248
    • Adler, M.1
  • 10
    • 34250286595 scopus 로고    scopus 로고
    • Adler, M., On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-de Vries equation, Invent. Math 50 (1979), 219-248. MR 80i:58026
    • MR , vol.80 I , pp. 58026
  • 11
    • 49149147606 scopus 로고    scopus 로고
    • Completely integrable systems, Euclidean Lie algebras and curves
    • Adler, M., van Moerbeke, P., Completely integrable systems, Euclidean Lie algebras and curves, Adv. Math. 38 (1980), 267-317. MR 83m:58041
    • (1980) Adv. Math. , vol.38 , pp. 267-317
    • Adler, M.1    Van Moerbeke, P.2
  • 12
    • 49149147606 scopus 로고    scopus 로고
    • Adler, M., van Moerbeke, P., Completely integrable systems, Euclidean Lie algebras and curves, Adv. Math. 38 (1980), 267-317. MR 83m:58041
    • MR , vol.83 M , pp. 58041
  • 14
    • 0040688795 scopus 로고    scopus 로고
    • Arnold, V.I., Mathematical Methods of Classical Mechanics, Springer-Verlag, 1978. MR 57:14033
    • MR , vol.57 , pp. 14033
  • 16
    • 0039503520 scopus 로고    scopus 로고
    • Arnold, V.I., Avez, A., Ergodic Problems of Classical Mechanics, W. A. Benjamin, Inc., New York, 1968. MR 38:1233
    • MR , vol.38 , pp. 1233
  • 17
    • 0003784355 scopus 로고    scopus 로고
    • Cambridge Univ. Press
    • Audin, M., Spinning Tops, Cambridge Univ. Press, 1996. MR 97i:58068
    • (1996) Spinning Tops
    • Audin, M.1
  • 18
    • 0040095276 scopus 로고    scopus 로고
    • Audin, M., Spinning Tops, Cambridge Univ. Press, 1996. MR 97i:58068
    • MR , vol.97 I , pp. 58068
  • 19
    • 84990617857 scopus 로고    scopus 로고
    • Scattering and inverse scattering for first order systems
    • Beals, R., Coifman, R.R., Scattering and inverse scattering for first order systems, Commun. Pure Appl. Math. 37 (1984), 39-90. MR 85f:34020
    • (1984) Commun. Pure Appl. Math. , vol.37 , pp. 39-90
    • Beals, R.1    Coifman, R.R.2
  • 20
    • 84990617857 scopus 로고    scopus 로고
    • Beals, R., Coifman, R.R., Scattering and inverse scattering for first order systems, Commun. Pure Appl. Math. 37 (1984), 39-90. MR 85f:34020
    • MR , vol.85 F , pp. 34020
  • 21
    • 0002754832 scopus 로고    scopus 로고
    • Inverse scattering and evolution equations
    • Beals, R., Coifman, R.R., Inverse scattering and evolution equations, Commun. Pure Appl. Math. 38 (1985), 29-42. MR 86f:35153
    • (1985) Commun. Pure Appl. Math. , vol.38 , pp. 29-42
    • Beals, R.1    Coifman, R.R.2
  • 22
    • 0002754832 scopus 로고    scopus 로고
    • Beals, R., Coifman, R.R., Inverse scattering and evolution equations, Commun. Pure Appl. Math. 38 (1985), 29-42. MR 86f:35153
    • MR , vol.86 F , pp. 35153
  • 23
    • 0002530625 scopus 로고    scopus 로고
    • Linear spectral problems, non-linear equations and the ∂̄-method
    • Beals, R., Coifman, R.R., Linear spectral problems, non-linear equations and the ∂̄-method, Inverse Problems 5 (1989), 87-130. MR 90f:35171
    • (1989) Inverse Problems , vol.5 , pp. 87-130
    • Beals, R.1    Coifman, R.R.2
  • 24
    • 0002530625 scopus 로고    scopus 로고
    • Beals, R., Coifman, R.R., Linear spectral problems, non-linear equations and the ∂̄-method, Inverse Problems 5 (1989), 87-130. MR 90f:35171
    • MR , vol.90 F , pp. 35171
  • 25
    • 0001323186 scopus 로고    scopus 로고
    • On the complete integrability of complete integrable systems
    • Beals, R., Sattinger, D.H., On the complete integrability of complete integrable systems, Commun. Math. Phys. 138 (1991), 409-436. MR 92m:58051
    • (1991) Commun. Math. Phys. , vol.138 , pp. 409-436
    • Beals, R.1    Sattinger, D.H.2
  • 26
    • 0001323186 scopus 로고    scopus 로고
    • Beals, R., Sattinger, D.H., On the complete integrability of complete integrable systems, Commun. Math. Phys. 138 (1991), 409-436. MR 92m:58051
    • MR , vol.92 M , pp. 58051
  • 28
    • 0039503567 scopus 로고    scopus 로고
    • Beals, R., Deift, P., Zhou, X., The inverse scattering transform on the line, in Important Developments in Soliton Theory, Springer, Berlin, 1993, pp. 7-32. MR 95k:34020
    • MR , vol.95 K , pp. 34020
  • 29
    • 0001650497 scopus 로고
    • Proof of the ergodic theorem
    • Birkhoff, G.D., Proof of the Ergodic Theorem, Proc. Nat. Acad. Sci. USA 17 (1931), 650-660.
    • (1931) Proc. Nat. Acad. Sci. USA , vol.17 , pp. 650-660
    • Birkhoff, G.D.1
  • 30
    • 0001119719 scopus 로고
    • The initial-value problem for the Korteveg-de Vries equation
    • Bona, J.L. and Smith, R., The Initial-Value Problem for the Korteveg-de Vries Equation, Philos. Trans. Royal Soc. London, Series A 278 (1975), 555-601. MR 52:6219
    • (1975) Philos. Trans. Royal Soc. London, Series A , vol.278 , pp. 555-601
    • Bona, J.L.1    Smith, R.2
  • 31
    • 0040688757 scopus 로고    scopus 로고
    • Bona, J.L. and Smith, R., The Initial-Value Problem for the Korteveg-de Vries Equation, Philos. Trans. Royal Soc. London, Series A 278 (1975), 555-601. MR 52:6219
    • MR , vol.52 , pp. 6219
  • 32
    • 0002741452 scopus 로고
    • A completely integrable model of classical field theory with nontrivial particle interaction in two-dimensional space-time. Questions in quantum field theory and statistical physocs
    • 229 (in Russian)
    • Budagov, A.S., A completely integrable model of classical field theory with nontrivial particle interaction in two-dimensional space-time. Questions in quantum field theory and statistical physocs, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 77 (1978), 24-56, 229 (in Russian). MR 80e:81053
    • (1978) Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) , vol.77 , pp. 24-56
    • Budagov, A.S.1
  • 33
    • 0040095278 scopus 로고    scopus 로고
    • Budagov, A.S., A completely integrable model of classical field theory with nontrivial particle interaction in two-dimensional space-time. Questions in quantum field theory and statistical physocs, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov (LOMI) 77 (1978), 24-56, 229 (in Russian). MR 80e:81053
    • MR , vol.80 E , pp. 81053
  • 35
    • 0041065707 scopus 로고    scopus 로고
    • Bullough, R.K., Caudrey, P.J., Solitons, Topics in Current Physics, vol. 117, Springer-Verlag, 1980. MR 82m:35001
    • MR , vol.82 M , pp. 35001
  • 37
    • 0039503564 scopus 로고    scopus 로고
    • Darboux, G., Leçons sur la théorie, générale, des surfaces, Chelsea, 1972. MR 53:81
    • MR , vol.53 , pp. 81
  • 40
    • 0040688792 scopus 로고    scopus 로고
    • Drazin, P.G., Johnson, R.S., Solitons: an introduction, Cambridge Univ. Press, 1989. MR 90j:35166
    • MR , vol.90 J , pp. 35166
  • 41
    • 0001603842 scopus 로고
    • Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of classical Yang-Baxter equations
    • Drinfel'd, V.G., Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of classical Yang-Baxter equations, Dokl. Akad. Nauk SSSR 268 (1983), 285-287; Trans. as Sov. Math. Doklady 27 (1983), 68-71. MR 841:58044
    • (1983) Dokl. Akad. Nauk SSSR , vol.268 , pp. 285-287
    • Drinfel'd, V.G.1
  • 42
    • 0040095279 scopus 로고
    • Drinfel'd, V.G., Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of classical Yang-Baxter equations, Dokl. Akad. Nauk SSSR 268 (1983), 285-287; Trans. as Sov. Math. Doklady 27 (1983), 68-71. MR 841:58044
    • (1983) Trans. As Sov. Math. Doklady , vol.27 , pp. 68-71
  • 43
    • 0039503563 scopus 로고    scopus 로고
    • Drinfel'd, V.G., Hamiltonian structures on Lie groups, Lie bialgebras and the geometric meaning of classical Yang-Baxter equations, Dokl. Akad. Nauk SSSR 268 (1983), 285-287; Trans. as Sov. Math. Doklady 27 (1983), 68-71. MR 841:58044
    • MR , vol.841 , pp. 58044
  • 44
    • 0002815036 scopus 로고
    • Equations of Korteweg-de Vries type and simple Lie algebras
    • Drinfel'd, V.G., and Sokolov, V.V., Equations of Korteweg-de Vries type and simple Lie algebras, Dokl. Akad. Nauk SSSR 258 (1981), 11-16; Trans. as Soviet Math. Dokl. 23, 457-462.
    • (1981) Dokl. Akad. Nauk SSSR , vol.258 , pp. 11-16
    • Drinfel'd, V.G.1    Sokolov, V.V.2
  • 45
    • 0040095240 scopus 로고    scopus 로고
    • Drinfel'd, V.G., and Sokolov, V.V., Equations of Korteweg-de Vries type and simple Lie algebras, Dokl. Akad. Nauk SSSR 258 (1981), 11-16; Trans. as Soviet Math. Dokl. 23, 457-462.
    • Trans. As Soviet Math. Dokl. , vol.23 , pp. 457-462
  • 46
    • 0039503522 scopus 로고    scopus 로고
    • MR 83k:58040
    • MR , vol.83 K , pp. 58040
  • 47
    • 0008531116 scopus 로고
    • Beweis dass ein mechanisches Normalsysteme im Allgemeinen quasiergodisch ist
    • Fermi, E., Beweis dass ein mechanisches Normalsysteme im Allgemeinen quasiergodisch ist, Phys, Zeit. 24 (1923), 261-265.
    • (1923) Phys, Zeit. , vol.24 , pp. 261-265
    • Fermi, E.1
  • 49
    • 0039503521 scopus 로고    scopus 로고
    • Faddeev, L.D., Takhtajan, L.A., Hamiltonian Methods in the Theory of Solitons, Springer-Verlag, 1987. MR 89m:58103
    • MR , vol.89 M , pp. 58103
  • 50
    • 0001942365 scopus 로고
    • Studies of nonlinear problems. I
    • Nonlinear Wave Motion, Amer. Math. Soc.
    • Fermi, E., Pasta, J., Ulam, S., Studies of Nonlinear Problems. I, in Nonlinear Wave Motion, Lectures in Applied Math., vol. 15, Amer. Math. Soc., 1974, pp. 143-155. MR 49:790
    • (1974) Lectures in Applied Math. , vol.15 , pp. 143-155
    • Fermi, E.1    Pasta, J.2    Ulam, S.3
  • 51
    • 0038910911 scopus 로고    scopus 로고
    • Fermi, E., Pasta, J., Ulam, S., Studies of Nonlinear Problems. I, in Nonlinear Wave Motion, Lectures in Applied Math., vol. 15, Amer. Math. Soc., 1974, pp. 143-155. MR 49:790
    • MR , vol.49 , pp. 790
  • 53
    • 48749145101 scopus 로고    scopus 로고
    • 1(1), Physica 9D (1983), 303-323. MR 86m:58067
    • MR , vol.86 M , pp. 58067
  • 55
    • 0038910938 scopus 로고
    • Graded Lie algebras and completely mtegrable dynamical systems
    • Frenkel, I.E., Reiman, A.G., Semenov-Tian-Shansky, M.A., Graded Lie algebras and completely mtegrable dynamical systems, Dokl. Akad. Nauk SSSR 247 (1979), 802-805; Trans. as Soviet Math. Dokl. 20 (1979), 811-814. MR 81c:58042
    • (1979) Dokl. Akad. Nauk SSSR , vol.247 , pp. 802-805
    • Frenkel, I.E.1    Reiman, A.G.2    Semenov-Tian-Shansky, M.A.3
  • 56
    • 0038910939 scopus 로고
    • Frenkel, I.E., Reiman, A.G., Semenov-Tian-Shansky, M.A., Graded Lie algebras and completely mtegrable dynamical systems, Dokl. Akad. Nauk SSSR 247 (1979), 802-805; Trans. as Soviet Math. Dokl. 20 (1979), 811-814. MR 81c:58042
    • (1979) Trans. As Soviet Math. Dokl. , vol.20 , pp. 811-814
  • 57
    • 0039503559 scopus 로고    scopus 로고
    • Frenkel, I.E., Reiman, A.G., Semenov-Tian-Shansky, M.A., Graded Lie algebras and completely mtegrable dynamical systems, Dokl. Akad. Nauk SSSR 247 (1979), 802-805; Trans. as Soviet Math. Dokl. 20 (1979), 811-814. MR 81c:58042
    • MR , vol.81 C , pp. 58042
  • 58
    • 36849102552 scopus 로고    scopus 로고
    • The Korteweg-de Vries Equation as a Hamiltonian system
    • Gardner, C.S., The Korteweg-de Vries Equation as a Hamiltonian system, J. Math. Physics 12 (1971), 1548-1551. MR 44:3615
    • (1971) J. Math. Physics , vol.12 , pp. 1548-1551
    • Gardner, C.S.1
  • 59
    • 36849102552 scopus 로고    scopus 로고
    • Gardner, C.S., The Korteweg-de Vries Equation as a Hamiltonian system, J. Math. Physics 12 (1971), 1548-1551. MR 44:3615
    • MR , vol.44 , pp. 3615
  • 62
    • 34250297237 scopus 로고    scopus 로고
    • Gel'fand, I.M., Dikii, L.A., Fractional Powers of Operators and Hamiltonian Systems, Funkcional'nyi Analiz i ego Prilozhenija 10 (1976). MR 55:6484
    • MR , vol.55 , pp. 6484
  • 63
    • 0001681528 scopus 로고
    • Hamiltonian operators and algebraic structures associated with them
    • Gel'fand, I.M., Dorfman, I. Ya, Hamiltonian operators and algebraic structures associated with them, Functional Anal. Appl. 13 (1979), 13-30, 96. MR 81c:58035
    • (1979) Functional Anal. Appl. , vol.13 , pp. 13-30
    • Gel'fand, I.M.1    Dorfman, I.Ya.2
  • 64
    • 0040688791 scopus 로고    scopus 로고
    • Gel'fand, I.M., Dorfman, I. Ya, Hamiltonian operators and algebraic structures associated with them, Functional Anal. Appl. 13 (1979), 13-30, 96. MR 81c:58035
    • MR , vol.81 C , pp. 58035
  • 65
    • 0001458591 scopus 로고
    • On the, determination of a differential equation from its spectral function
    • Gel'fand, I.M., Levitan, B. M., On the, determination of a differential equation from its spectral function, Izv. Akad. Nauk SSSR Ser. Mat. 15 (1951), 309-360. MR 13:558f
    • (1951) Izv. Akad. Nauk SSSR Ser. Mat. , vol.15 , pp. 309-360
    • Gel'fand, I.M.1    Levitan, B.M.2
  • 66
    • 4243930851 scopus 로고    scopus 로고
    • Gel'fand, I.M., Levitan, B. M., On the, determination of a differential equation from its spectral function, Izv. Akad. Nauk SSSR Ser. Mat. 15 (1951), 309-360. MR 13:558f
    • MR , vol.13
  • 67
    • 0000774509 scopus 로고
    • Motion of a vortex filament and its relation to elastic
    • Hasimoto, H., Motion of a vortex filament and its relation to elastic, J. Phys. Soc. Japan 31 (1971), 293-295.
    • (1971) J. Phys. Soc. Japan , vol.31 , pp. 293-295
    • Hasimoto, H.1
  • 69
    • 0002362136 scopus 로고
    • On the Cauchy problem for the (Generalized) Korteweg-de vries equation
    • Kato, T., On the Cauchy Problem for the (Generalized) Korteweg-de Vries Equation, Studies in Applied Math., Adv. in Math. Supp. Stud. 8 (1983), 93-128.
    • (1983) Studies in Applied Math., Adv. in Math. Supp. Stud. , vol.8 , pp. 93-128
    • Kato, T.1
  • 70
    • 0038910905 scopus 로고    scopus 로고
    • MR 86f:35160
    • MR , vol.86 F , pp. 35160
  • 71
    • 0003123140 scopus 로고
    • Quasi-linear equations of evolution, with applications to partial differential equations
    • Springer-Verlag, Berlin and New York
    • Kato, T., Quasi-linear equations of evolution, with applications to partial differential equations, Lecture Notes in Math., vol. 448, Springer-Verlag, Berlin and New York, 1975, pp. 25-70. MR 53:11252
    • (1975) Lecture Notes in Math. , vol.448 , pp. 25-70
    • Kato, T.1
  • 72
    • 0039503560 scopus 로고    scopus 로고
    • Kato, T., Quasi-linear equations of evolution, with applications to partial differential equations, Lecture Notes in Math., vol. 448, Springer-Verlag, Berlin and New York, 1975, pp. 25-70. MR 53:11252
    • MR , vol.53 , pp. 11252
  • 73
    • 0001524186 scopus 로고
    • On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves
    • Korteweg, D.J., de Vries, G., On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves, Philos. Mag. Ser. 5 39 (1895), 422-443.
    • (1895) Philos. Mag. Ser. 5 , vol.39 , pp. 422-443
    • Korteweg, D.J.1    De Vries, G.2
  • 74
    • 0000876641 scopus 로고    scopus 로고
    • The solution to a generalized toda lattice and representation theory
    • Kostant, B., The solution to a generalized Toda lattice and representation theory, Adv. Math. 34 (1979), 195-338. MR 82f:58045
    • (1979) Adv. Math. , vol.34 , pp. 195-338
    • Kostant, B.1
  • 75
    • 0000876641 scopus 로고    scopus 로고
    • Kostant, B., The solution to a generalized Toda lattice and representation theory, Adv. Math. 34 (1979), 195-338. MR 82f:58045
    • MR , vol.82 F , pp. 58045
  • 76
    • 0003043085 scopus 로고
    • The determination of the scattering potential from the spectral measure function, III
    • Kay, B., Moses, H.E., The determination of the scattering potential from the spectral measure function, III, Nuovo Cim. 3 (1956), 276-304.
    • (1956) Nuovo Cim. , vol.3 , pp. 276-304
    • Kay, B.1    Moses, H.E.2
  • 79
    • 0038910910 scopus 로고    scopus 로고
    • Lamb, G.L., Jr., Elements of Soliton Theory, John Wiley & Sons, New York, 1980. MR 82f:35165
    • MR , vol.82 F , pp. 35165
  • 80
    • 84981754671 scopus 로고    scopus 로고
    • Integrals of nonlinear equations of evolution and solitary waves
    • Lax, P.D., Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure. Appl. Math. 21 (1968), 467-490. MR 38:3620
    • (1968) Comm. Pure. Appl. Math. , vol.21 , pp. 467-490
    • Lax, P.D.1
  • 81
    • 84981754671 scopus 로고    scopus 로고
    • Lax, P.D., Integrals of nonlinear equations of evolution and solitary waves, Comm. Pure. Appl. Math. 21 (1968), 467-490. MR 38:3620
    • MR , vol.38 , pp. 3620
  • 82
    • 0003116194 scopus 로고
    • Periodic solutions of the KdV equations
    • Nonlinear Wave Motion, Amer. Math. Soc.
    • Lax, P.D., Periodic Solutions of the KdV Equations, in Nonlinear Wave Motion, Lectures in Applied Math., vol. 15, Amer. Math. Soc., 1974, pp. 85-96. MR 49:9384
    • (1974) Lectures in Applied Math. , vol.15 , pp. 85-96
    • Lax, P.D.1
  • 83
    • 0040095247 scopus 로고    scopus 로고
    • Lax, P.D., Periodic Solutions of the KdV Equations, in Nonlinear Wave Motion, Lectures in Applied Math., vol. 15, Amer. Math. Soc., 1974, pp. 85-96. MR 49:9384
    • MR , vol.49 , pp. 9384
  • 84
    • 0037980040 scopus 로고    scopus 로고
    • Outline of a theory of the KdV equation
    • Recent Mathematical Methods in Nonlinear Wave Propogation, Springer-Verlag, Berlin and New York
    • Lax, P.D., Outline of a theory of the KdV equation, in Recent Mathematical Methods in Nonlinear Wave Propogation, Lecture Notes in Math., vol. 1640, Springer-Verlag, Berlin and New York, 1996, pp. 70-102.
    • (1996) Lecture Notes in Math. , vol.1640 , pp. 70-102
    • Lax, P.D.1
  • 85
    • 0039503556 scopus 로고    scopus 로고
    • Nonlinear waves, nonlinear optics, and your communications future
    • Springer-Verlag New York, Inc.
    • Luther, G.G., Alber, M.S., Nonlinear Waves, Nonlinear Optics, and Your Communications Future, in Nonlinear Science Today, Springer-Verlag New York, Inc., 1997.
    • (1997) Nonlinear Science Today
    • Luther, G.G.1    Alber, M.S.2
  • 86
    • 0000861291 scopus 로고
    • On the reconstruction of the potential energy from phases of the scattered waves
    • Marchenko, V.A., On the reconstruction of the potential energy from phases of the scattered waves, Dokl. Akad. Nauk SSSR, 104 (1955), 695-698.
    • (1955) Dokl. Akad. Nauk SSSR , vol.104 , pp. 695-698
    • Marchenko, V.A.1
  • 88
    • 0040095272 scopus 로고    scopus 로고
    • Newell, A.C., Solitons in Mathematics and Physics, SIAM, CBMS-NSF vol. 48, 1985. MR 87h:35314
    • MR , vol.87 H , pp. 35314
  • 90
    • 0039503557 scopus 로고    scopus 로고
    • Novikov, S., Manakov, S., Pitaevskii, L.B., Zakharov, V.E., Theory of Solitons, Plenum, New York, 1984. MR 86k:35142
    • MR , vol.86 K , pp. 35142
  • 91
    • 0001417119 scopus 로고
    • Measure preserving homeomorphisms and metrical transitivity
    • Oxtoby, J.C., Ulam, S.M., Measure Preserving Homeomorphisms and Metrical Transitivity, Annals of Math. 42 (1941), 874-920. MR 3:211b
    • (1941) Annals of Math. , vol.42 , pp. 874-920
    • Oxtoby, J.C.1    Ulam, S.M.2
  • 92
    • 4243882380 scopus 로고    scopus 로고
    • Oxtoby, J.C., Ulam, S.M., Measure Preserving Homeomorphisms and Metrical Transitivity, Annals of Math. 42 (1941), 874-920. MR 3:211b
    • MR , vol.3
  • 93
    • 0003288058 scopus 로고
    • Critical point theory and submanifold geometry
    • Springer-Verlag, Berlin and New York
    • Palais, R.S., and Terng, C.L., Critical Point Theory and Submanifold Geometry, Lecture Notes in Math., vol. 1353, Springer-Verlag, Berlin and New York, 1988. MR 90c:53143
    • (1988) Lecture Notes in Math. , vol.1353
    • Palais, R.S.1    Terng, C.L.2
  • 94
    • 0039503524 scopus 로고    scopus 로고
    • Palais, R.S., and Terng, C.L., Critical Point Theory and Submanifold Geometry, Lecture Notes in Math., vol. 1353, Springer-Verlag, Berlin and New York, 1988. MR 90c:53143
    • MR , vol.90 C , pp. 53143
  • 96
    • 0040688790 scopus 로고    scopus 로고
    • Perelomov, A.M., Integrable Systems of Classical Mechanics and Lie Algebras, Birkhäuser Verlag, Basel, 1990. MR 91g:58127
    • MR , vol.91 G , pp. 58127
  • 97
    • 0003863511 scopus 로고
    • Oxford Science Publ., Clarendon Press, Oxford
    • Pressley, A. and Segal, G. B., Loop Groups, Oxford Science Publ., Clarendon Press, Oxford, 1986. MR 88i:22049
    • (1986) Loop Groups
    • Pressley, A.1    Segal, G.B.2
  • 98
    • 0038832785 scopus 로고    scopus 로고
    • Pressley, A. and Segal, G. B., Loop Groups, Oxford Science Publ., Clarendon Press, Oxford, 1986. MR 88i:22049
    • MR , vol.88 I , pp. 22049
  • 99
    • 0000978499 scopus 로고
    • Current algebras and non-linear partial differential equations
    • Reyman, A.C., Semenov-Tian-Shansky, M.A., Current algebras and non-linear partial differential equations, Sov. Math., Dokl. 21 (1980), 630-634.
    • (1980) Sov. Math., Dokl. , vol.21 , pp. 630-634
    • Reyman, A.C.1    Semenov-Tian-Shansky, M.A.2
  • 100
    • 0001717693 scopus 로고
    • Rediscovery of the Da Rios equation
    • Rica, R.L., Rediscovery of the Da Rios Equation, Nature 352 (1991), 561-562.
    • (1991) Nature , vol.352 , pp. 561-562
    • Rica, R.L.1
  • 102
    • 0022011039 scopus 로고    scopus 로고
    • Hamiltonian hierarchies on semi-simple Lie algebras
    • Sattinger, D.H., Hamiltonian hierarchies on semi-simple Lie algebras, Stud. Appl. Math. 72 (1985), 65-86. MR 86b:58063
    • (1985) Stud. Appl. Math. , vol.72 , pp. 65-86
    • Sattinger, D.H.1
  • 103
    • 0022011039 scopus 로고    scopus 로고
    • Sattinger, D.H., Hamiltonian hierarchies on semi-simple Lie algebras, Stud. Appl. Math. 72 (1985), 65-86. MR 86b:58063
    • MR , vol.86 B , pp. 58063
  • 104
    • 51249179487 scopus 로고    scopus 로고
    • Loop groups and equations of KdV type
    • Segal, G., Wilson, G., Loop groups and equations of KdV type, Publ. Math. IHES 61 (1985), 5-65. MR 87b:58039
    • (1985) Publ. Math. IHES , vol.61 , pp. 5-65
    • Segal, G.1    Wilson, G.2
  • 105
    • 51249179487 scopus 로고    scopus 로고
    • Segal, G., Wilson, G., Loop groups and equations of KdV type, Publ. Math. IHES 61 (1985), 5-65. MR 87b:58039
    • MR , vol.87 B , pp. 58039
  • 106
    • 85024263510 scopus 로고    scopus 로고
    • Dressing transformations and poisson group actions
    • Semenov-Tian-Shansky, M.A., Dressing transformations and Poisson group actions, Publ. RIMS Kyoto Univ. 21 (1985), 1237-1260. MR 88b:58057
    • (1985) Publ. RIMS Kyoto Univ. , vol.21 , pp. 1237-1260
    • Semenov-Tian-Shansky, M.A.1
  • 107
    • 85024263510 scopus 로고    scopus 로고
    • Semenov-Tian-Shansky, M.A., Dressing transformations and Poisson group actions, Publ. RIMS Kyoto Univ. 21 (1985), 1237-1260. MR 88b:58057
    • MR , vol.88 B , pp. 58057
  • 108
    • 0008372461 scopus 로고
    • Classical r-matrices, Lax equations, poisson lie groups, and dressing transformations
    • Springer-Verlag
    • Semenov-Tian-Shansky, M.A., Classical r-matrices, Lax equations, Poisson Lie groups, and dressing transformations, Lecture Notes in Physics, Springer-Verlag, vol. 280, 1987, pp. 174-214.
    • (1987) Lecture Notes in Physics , vol.280 , pp. 174-214
    • Semenov-Tian-Shansky, M.A.1
  • 109
    • 0039503554 scopus 로고    scopus 로고
    • MR 89g:58098
    • MR , vol.89 G , pp. 58098
  • 110
    • 0002208971 scopus 로고
    • An inverse scattering problem
    • Shabat, A.B., An inverse scattering problem, Diff. Uravneniya 15 (1979), 1824-1834; Trans. in Diff. Equ. 15 (1980), 1299-1307. MR 81m:34026
    • (1979) Diff. Uravneniya , vol.15 , pp. 1824-1834
    • Shabat, A.B.1
  • 111
    • 0040095241 scopus 로고
    • Shabat, A.B., An inverse scattering problem, Diff. Uravneniya 15 (1979), 1824-1834; Trans. in Diff. Equ. 15 (1980), 1299-1307. MR 81m:34026
    • (1980) Trans. in Diff. Equ. , vol.15 , pp. 1299-1307
  • 112
    • 0039503553 scopus 로고    scopus 로고
    • Shabat, A.B., An inverse scattering problem, Diff. Uravneniya 15 (1979), 1824-1834; Trans. in Diff. Equ. 15 (1980), 1299-1307. MR 81m:34026
    • MR , vol.81 M , pp. 34026
  • 113
    • 0001518684 scopus 로고
    • On the construction and comparison of difference schemes
    • Strang, G., On the Construction and Comparison of Difference Schemes, SIAM J. Numerical Analysis 5 (1968), 506-517. MR 38:4057
    • (1968) SIAM J. Numerical Analysis , vol.5 , pp. 506-517
    • Strang, G.1
  • 114
    • 0040688788 scopus 로고    scopus 로고
    • Strang, G., On the Construction and Comparison of Difference Schemes, SIAM J. Numerical Analysis 5 (1968), 506-517. MR 38:4057
    • MR , vol.38 , pp. 4057
  • 115
    • 34250248977 scopus 로고    scopus 로고
    • Systems of toda type, inverse spectral problems, and representation theory
    • Symes, W.W., Systems of Toda type, Inverse spectral problems, and representation theory, Inventiones Math. 59 (1980), 13-51. MR 81g:58019
    • (1980) Inventiones Math. , vol.59 , pp. 13-51
    • Symes, W.W.1
  • 116
    • 34250248977 scopus 로고    scopus 로고
    • Symes, W.W., Systems of Toda type, Inverse spectral problems, and representation theory, Inventiones Math. 59 (1980), 13-51. MR 81g:58019
    • MR , vol.81 G , pp. 58019
  • 117
    • 0000251609 scopus 로고
    • Numerical solutions of the Korteweg-de Vries equations and its generalizations by the split-step fourier method
    • Nonlinear Wave Motion, Amer. Math. Soc.
    • Tappert, F., Numerical Solutions of the Korteweg-de Vries Equations and its Generalizations by the Split-Step Fourier Method, in Nonlinear Wave Motion, Lectures in Applied Math., vol. 15, Amer. Math. Soc., 1974, pp. 215-216. MR 49:790
    • (1974) Lectures in Applied Math. , vol.15 , pp. 215-216
    • Tappert, F.1
  • 118
    • 0038910911 scopus 로고    scopus 로고
    • Tappert, F., Numerical Solutions of the Korteweg-de Vries Equations and its Generalizations by the Split-Step Fourier Method, in Nonlinear Wave Motion, Lectures in Applied Math., vol. 15, Amer. Math. Soc., 1974, pp. 215-216. MR 49:790
    • MR , vol.49 , pp. 790
  • 119
    • 0000097612 scopus 로고
    • A higher dimensional generalization of the Sine-Gordon equation and its soliton theory
    • Terng, C.L., A higher dimensional generalization of the Sine-Gordon equation and its soliton theory, Ann. Math. 111 (1980), 491-510. MR 82J.-58069
    • (1980) Ann. Math. , vol.111 , pp. 491-510
    • Terng, C.L.1
  • 120
    • 0040095245 scopus 로고    scopus 로고
    • Terng, C.L., A higher dimensional generalization of the Sine-Gordon equation and its soliton theory, Ann. Math. 111 (1980), 491-510. MR 82J.-58069
    • MR , vol.82 J , pp. 58069
  • 121
    • 0031065010 scopus 로고    scopus 로고
    • Soliton equations and differential geometry
    • Terng, C.L., Soliton equations and differential geometry, J. Differential Geometry 45 (1997), 407-445. CMP 97:13
    • (1997) J. Differential Geometry , vol.45 , pp. 407-445
    • Terng, C.L.1
  • 122
    • 0031065010 scopus 로고    scopus 로고
    • Terng, C.L., Soliton equations and differential geometry, J. Differential Geometry 45 (1997), 407-445. CMP 97:13
    • CMP , vol.97 , pp. 13
  • 125
    • 84972545531 scopus 로고    scopus 로고
    • Harmonic, maps into Lie group (classical solutions of the chiral model)
    • Uhlenbeck, K., Harmonic, maps into Lie group (classical solutions of the chiral model), J. Differential Geometry 30 (1989), 1-50. MR 90g:58028
    • (1989) J. Differential Geometry , vol.30 , pp. 1-50
    • Uhlenbeck, K.1
  • 126
    • 84972545531 scopus 로고    scopus 로고
    • Uhlenbeck, K., Harmonic, maps into Lie group (classical solutions of the chiral model), J. Differential Geometry 30 (1989), 1-50. MR 90g:58028
    • MR , vol.90 G , pp. 58028
  • 127
    • 0001286387 scopus 로고    scopus 로고
    • On the connection between harmonic maps and the self-dual Yang-mills and the Sine-Gordon equations
    • Uhlenbeck, K., On the connection between harmonic maps and the self-dual Yang-Mills and the Sine-Gordon equations, J. Geom. Phys. 8 (1992), 283-316. MR 93f:58050
    • (1992) J. Geom. Phys. , vol.8 , pp. 283-316
    • Uhlenbeck, K.1
  • 128
    • 0001286387 scopus 로고    scopus 로고
    • Uhlenbeck, K., On the connection between harmonic maps and the self-dual Yang-Mills and the Sine-Gordon equations, J. Geom. Phys. 8 (1992), 283-316. MR 93f:58050
    • MR , vol.93 F , pp. 58050
  • 130
    • 0038910907 scopus 로고    scopus 로고
    • Ulam, S. M., Adventures of a Mathematician, Univ. of Calif. Press, 1991. MR 58:4954
    • MR , vol.58 , pp. 4954
  • 131
    • 0007690397 scopus 로고    scopus 로고
    • The modified Korteweg-de Vries equation
    • Wadati, M., The modified Korteweg-de Vries equation, J. Phys. Soc. Japan 34 (1973), 1289-1296. MR 51:7472
    • (1973) J. Phys. Soc. Japan , vol.34 , pp. 1289-1296
    • Wadati, M.1
  • 132
    • 0007690397 scopus 로고    scopus 로고
    • Wadati, M., The modified Korteweg-de Vries equation, J. Phys. Soc. Japan 34 (1973), 1289-1296. MR 51:7472
    • MR , vol.51 , pp. 7472
  • 133
    • 21244460720 scopus 로고    scopus 로고
    • The modified Lax equations and two dimensional Toda lattice equations associated with simple lie algebras
    • Wilson, G., The modified Lax equations and two dimensional Toda lattice equations associated with simple Lie algebras, Ergodic Theory and Dynamical Systems I 30 (1981), 361-380. MR 84b:58058
    • (1981) Ergodic Theory and Dynamical Systems I , vol.30 , pp. 361-380
    • Wilson, G.1
  • 134
    • 21244460720 scopus 로고    scopus 로고
    • Wilson, G., The modified Lax equations and two dimensional Toda lattice equations associated with simple Lie algebras, Ergodic Theory and Dynamical Systems I 30 (1981), 361-380. MR 84b:58058
    • MR , vol.84 B , pp. 58058
  • 135
    • 33846361348 scopus 로고
    • Interaction of solitons in a collisionless plasma and the recurrence of initial states
    • Zabusky, N.J., Kruskal, M.D., Interaction of solitons in a collisionless plasma and the recurrence of initial states, Physics Rev. Lett, 15 (1965), 240-243.
    • (1965) Physics Rev. Lett , vol.15 , pp. 240-243
    • Zabusky, N.J.1    Kruskal, M.D.2
  • 136
    • 0002161530 scopus 로고
    • Korteweg-de Vries equation is a fully integrable Hamiltonian system
    • Zakharov, V.E., Faddeev, L.D., Korteweg-de Vries equation is a fully integrable Hamiltonian system, Funktsional Anal. i Prilozhen 5 (1971), 18-27. MR 46:2270
    • (1971) Funktsional Anal. I Prilozhen , vol.5 , pp. 18-27
    • Zakharov, V.E.1    Faddeev, L.D.2
  • 137
    • 0040688760 scopus 로고    scopus 로고
    • Zakharov, V.E., Faddeev, L.D., Korteweg-de Vries equation is a fully integrable Hamiltonian system, Funktsional Anal. i Prilozhen 5 (1971), 18-27. MR 46:2270
    • MR , vol.46 , pp. 2270
  • 138
    • 0000018057 scopus 로고
    • On resonant interaction of wave packets in non-linear media
    • Zakharov, V.E., Manakov, S.V., On resonant interaction of wave packets in non-linear media, JETP Letters 18 (1973), 243-247.
    • (1973) JETP Letters , vol.18 , pp. 243-247
    • Zakharov, V.E.1    Manakov, S.V.2
  • 139
    • 0040095238 scopus 로고
    • The theory of resonance interaction of wave packets in non-linear media
    • Zakharov, V.E., Manakov, S.V., The theory of resonance interaction of wave packets in non-linear media, Sov. Phys. JETP 42 (1975), 842-850. MR 54:14617
    • (1975) Sov. Phys. JETP , vol.42 , pp. 842-850
    • Zakharov, V.E.1    Manakov, S.V.2
  • 140
    • 0040095244 scopus 로고    scopus 로고
    • Zakharov, V.E., Manakov, S.V., The theory of resonance interaction of wave packets in non-linear media, Sov. Phys. JETP 42 (1975), 842-850. MR 54:14617
    • MR , vol.54 , pp. 14617
  • 141
    • 0005126128 scopus 로고
    • Example of nontrivial interaction of solitons in two-dimensional classical field theory
    • Zakharov, V.E., Mikhailov, A.V., Example of nontrivial interaction of solitons in two-dimensional classical field theory, JETP Letters 27 (1978), 42-46.
    • (1978) JETP Letters , vol.27 , pp. 42-46
    • Zakharov, V.E.1    Mikhailov, A.V.2
  • 142
    • 0000476712 scopus 로고
    • Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method
    • Zakharov, V.E., Mikhailov, A.V., Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method, Soviet Physics JETP 47 (1978), 1017-1027. MR 80c:81115
    • (1978) Soviet Physics JETP , vol.47 , pp. 1017-1027
    • Zakharov, V.E.1    Mikhailov, A.V.2
  • 143
    • 0040688759 scopus 로고    scopus 로고
    • Zakharov, V.E., Mikhailov, A.V., Relativistically invariant two-dimensional models of field theory which are integrable by means of the inverse scattering problem method, Soviet Physics JETP 47 (1978), 1017-1027. MR 80c:81115
    • MR , vol.80 C , pp. 81115
  • 144
    • 0002557939 scopus 로고
    • Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media
    • Zakharov, V.E., Shabat, A.B., Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Sov. Phys. JETP 34 (1972), 62-69. MR 53:9966
    • (1972) Sov. Phys. JETP , vol.34 , pp. 62-69
    • Zakharov, V.E.1    Shabat, A.B.2
  • 145
    • 0039503523 scopus 로고    scopus 로고
    • Zakharov, V.E., Shabat, A.B., Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Sov. Phys. JETP 34 (1972), 62-69. MR 53:9966
    • MR , vol.53 , pp. 9966


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.