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Volumn 40, Issue 11, 1999, Pages 5749-5786

Nonisospectral scattering problems: A key to integrable hierarchies

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EID: 0033240091     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.533055     Document Type: Article
Times cited : (103)

References (46)
  • 2
    • 0000440099 scopus 로고
    • Exact theory of the two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media
    • V. E. Zakharov and A. B. Shabat, "Exact theory of the two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media." Zh. Eksp. Teor. Fiz. 61, 118-134 (1971); Sov. Phys. JETP 34, 62-69 (1972).
    • (1971) Zh. Eksp. Teor. Fiz. , vol.61 , pp. 118-134
    • Zakharov, V.E.1    Shabat, A.B.2
  • 3
    • 0009296146 scopus 로고
    • V. E. Zakharov and A. B. Shabat, "Exact theory of the two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media." Zh. Eksp. Teor. Fiz. 61, 118-134 (1971); Sov. Phys. JETP 34, 62-69 (1972).
    • (1972) Sov. Phys. JETP , vol.34 , pp. 62-69
  • 4
    • 0009372301 scopus 로고
    • A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem, I
    • V. E. Zakharov and A. B. Shabat, "A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem, I," Funk. Anal. Pril. 8, 43-53 (1974); Funct. Anal. Appl. 8, 266-235 (1974).
    • (1974) Funk. Anal. Pril. , vol.8 , pp. 43-53
    • Zakharov, V.E.1    Shabat, A.B.2
  • 5
    • 0009372301 scopus 로고
    • V. E. Zakharov and A. B. Shabat, "A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem, I," Funk. Anal. Pril. 8, 43-53 (1974); Funct. Anal. Appl. 8, 266-235 (1974).
    • (1974) Funct. Anal. Appl. , vol.8 , pp. 266-1235
  • 6
    • 0000314031 scopus 로고
    • Analytic solution of the two-dimensional Korteweg-de Vries equation
    • V. S. Dryuma, "Analytic solution of the two-dimensional Korteweg-de Vries equation," Zh. Eksp. Teor. Fiz. Pis'ma Red. 19, 753-755 (1974); Sov. Phys. JETP Lett. 19, 387-388 (1974).
    • (1974) Zh. Eksp. Teor. Fiz. Pis'ma Red. , vol.19 , pp. 753-755
    • Dryuma, V.S.1
  • 7
    • 0015958451 scopus 로고
    • V. S. Dryuma, "Analytic solution of the two-dimensional Korteweg-de Vries equation," Zh. Eksp. Teor. Fiz. Pis'ma Red. 19, 753-755 (1974); Sov. Phys. JETP Lett. 19, 387-388 (1974).
    • (1974) Sov. Phys. JETP Lett. , vol.19 , pp. 387-388
  • 8
    • 34250256469 scopus 로고
    • Monodromy and spectrum preserving deformations, I
    • H. Flaschka and A. C. Newell, "Monodromy and spectrum preserving deformations, I," Commun. Math. Phys. 76, 65-116 (1980).
    • (1980) Commun. Math. Phys. , vol.76 , pp. 65-116
    • Flaschka, H.1    Newell, A.C.2
  • 9
    • 51249191266 scopus 로고
    • A method to generate solvable nonlinear evolution equations
    • F. Calogero, "A method to generate solvable nonlinear evolution equations," Lett. Nuovo Cimento 14, 443-447 (1975).
    • (1975) Lett. Nuovo Cimento , vol.14 , pp. 443-447
    • Calogero, F.1
  • 11
    • 0002001745 scopus 로고
    • Overturning solitons in two-dimensional integrable equations
    • O. I. Bogoyavlenskii, "Overturning solitons in two-dimensional integrable equations," Usp. Mat. Nauk 45, 17-77 (1990); Russ. Math. Surveys 45, 1-86 (1990).
    • (1990) Usp. Mat. Nauk , vol.45 , pp. 17-77
  • 12
    • 0039712870 scopus 로고
    • O. I. Bogoyavlenskii, "Overturning solitons in two-dimensional integrable equations," Usp. Mat. Nauk 45, 17-77 (1990); Russ. Math. Surveys 45, 1-86 (1990).
    • (1990) Russ. Math. Surveys , vol.45 , pp. 1-86
  • 13
    • 0000983519 scopus 로고
    • The inverse scattering method
    • edited by R. K. Bullough and P. J. Caudrey Springer, Berlin
    • V. E. Zakharov, "The inverse scattering method," in Solitons, edited by R. K. Bullough and P. J. Caudrey (Springer, Berlin. 1980).
    • (1980) Solitons
    • Zakharov, V.E.1
  • 14
    • 0030541599 scopus 로고    scopus 로고
    • The singular manifold method revisited
    • A. Pickering, "The singular manifold method revisited," J. Math. Phys. 37, 1894-1927 (1996).
    • (1996) J. Math. Phys. , vol.37 , pp. 1894-1927
    • Pickering, A.1
  • 15
    • 0001029269 scopus 로고    scopus 로고
    • Multicomponent equations associated to nonisospectral scattering problems
    • P. A. Clarkson, P. R. Gordoa, and A. Pickering, "Multicomponent equations associated to nonisospectral scattering problems," Inverse Probl. 13, 1463-1476 (1997).
    • (1997) Inverse Probl. , vol.13 , pp. 1463-1476
    • Clarkson, P.A.1    Gordoa, P.R.2    Pickering, A.3
  • 16
    • 0001820561 scopus 로고
    • Wave solutions of a 2 + 1-dimensional generalization of the nonlinear schrodinger equation
    • I. A. B. Strachan, "Wave solutions of a 2 + 1-dimensional generalization of the nonlinear Schrodinger equation," Inverse Probl. 8, L21-L27 (1992).
    • (1992) Inverse Probl. , vol.8
    • Strachan, I.A.B.1
  • 17
    • 21344494637 scopus 로고
    • Symmetries of a 2+ 1-dimensional breaking soliton equation
    • Yi-shen Li and You-jin Zhang, "Symmetries of a 2+ 1-dimensional breaking soliton equation," J. Phys. A 26, 7487-7494 (1993).
    • (1993) J. Phys. A , vol.26 , pp. 7487-7494
    • Yi-Shen, L.1    Zhang, Y.-J.2
  • 18
    • 0344063024 scopus 로고
    • On the integrable variant of the Boussinesq system: Painlevé property, rational solutions, a related many-body system, and equivalence with the AKNS hierarchy
    • R. L. Sachs, "On the integrable variant of the Boussinesq system: Painlevé property, rational solutions, a related many-body system, and equivalence with the AKNS hierarchy," Physica D 30, 1-27 (1988).
    • (1988) Physica D , vol.30 , pp. 1-27
    • Sachs, R.L.1
  • 19
    • 34249831181 scopus 로고
    • On nonisospectral flows, Painlevé equations, and symmetries of differential and difference equations
    • D. Levi, O. Ragnisco, and M. A. Rodriguez, "On nonisospectral flows, Painlevé equations, and symmetries of differential and difference equations," Teor. Mat. Fiz. 93, 473-480 (1992). Theor. Math. Phys. 93, 1409-1414 (1993).
    • (1992) Teor. Mat. Fiz. , vol.93 , pp. 473-480
    • Levi, D.1    Ragnisco, O.2    Rodriguez, M.A.3
  • 20
    • 34249831181 scopus 로고
    • D. Levi, O. Ragnisco, and M. A. Rodriguez, "On nonisospectral flows, Painlevé equations, and symmetries of differential and difference equations," Teor. Mat. Fiz. 93, 473-480 (1992). Theor. Math. Phys. 93, 1409-1414 (1993).
    • (1993) Theor. Math. Phys. , vol.93 , pp. 1409-1414
  • 21
    • 0008442554 scopus 로고
    • Inverse scattering method with variable spectral parameter
    • S. P. Burtsev, V. E. Zakharov, and A. V. Mikhailov, "Inverse scattering method with variable spectral parameter," Teor. Mat. Fiz. 70, 323-341 (1987).
    • (1987) Teor. Mat. Fiz. , vol.70 , pp. 323-341
    • Burtsev, S.P.1    Zakharov, V.E.2    Mikhailov, A.V.3
  • 23
    • 0001471498 scopus 로고
    • Some remarkable nonlinear transformations
    • A. P. Fordy and J. Gibbons, "Some remarkable nonlinear transformations," Phys. Lett. A 75, 325-325 (1980).
    • (1980) Phys. Lett. A , vol.75 , pp. 325-325
    • Fordy, A.P.1    Gibbons, J.2
  • 24
    • 0001395372 scopus 로고
    • A method for finding N-soliton solutions of the KdV equation and KdV-type equation
    • K. Sawada and T. Kotera, "A method for finding N-soliton solutions of the KdV equation and KdV-type equation," Prog. Theor. Phys. 51, 1355-1367 (1974).
    • (1974) Prog. Theor. Phys. , vol.51 , pp. 1355-1367
    • Sawada, K.1    Kotera, T.2
  • 26
    • 0002361867 scopus 로고    scopus 로고
    • Nonautonomous Hénon-Heiles systems
    • A. N. W. Hone, "Nonautonomous Hénon-Heiles systems," Physica D 118, 1-16 (1998).
    • (1998) Physica D , vol.118 , pp. 1-16
    • Hone, A.N.W.1
  • 28
    • 36749108571 scopus 로고
    • Evolution equations possessing infinitely many symmetries
    • P. J. Olver, "Evolution equations possessing infinitely many symmetries," J. Math. Phys. 18, 1212-1215 (1977).
    • (1977) J. Math. Phys. , vol.18 , pp. 1212-1215
    • Olver, P.J.1
  • 29
    • 0016369301 scopus 로고
    • The inverse scattering transform: Fourier analysis for nonlinear problems
    • M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, "The inverse scattering transform: Fourier analysis for nonlinear problems," Stud. Appl. Math. 53, 249-315 (1974).
    • (1974) Stud. Appl. Math. , vol.53 , pp. 249-315
    • Ablowitz, M.J.1    Kaup, D.J.2    Newell, A.C.3    Segur, H.4
  • 31
    • 0000103584 scopus 로고
    • Nonisospectral deformations and darboux transformations for the third order spectral problem
    • D. Levi and O. Ragnisco, "Nonisospectral deformations and Darboux transformations for the third order spectral problem," Inverse Probl. 4, 815-828 (1988).
    • (1988) Inverse Probl. , vol.4 , pp. 815-828
    • Levi, D.1    Ragnisco, O.2
  • 32
    • 0018495943 scopus 로고
    • Rational solutions of Painlevé equations
    • H. Airault, "Rational solutions of Painlevé equations," Stud. Appl. Math. 61, 31-53 (1979).
    • (1979) Stud. Appl. Math. , vol.61 , pp. 31-53
    • Airault, H.1
  • 33
    • 0041577427 scopus 로고    scopus 로고
    • The first and second Painlevé equations of higher order and some relations between them
    • N. A. Kudryashov, "The first and second Painlevé equations of higher order and some relations between them," Phys. Lett. A 224, 353-360 (1997).
    • (1997) Phys. Lett. A , vol.224 , pp. 353-360
    • Kudryashov, N.A.1
  • 34
    • 0039528278 scopus 로고    scopus 로고
    • Bäcklund transformations for the second Painlevé hierarchy: A modified truncation approach
    • P. A. Clarkson, N. Joshi, and A. Pickering, "Bäcklund transformations for the second Painlevé hierarchy: A modified truncation approach," Inverse Probl. 15, 175-187 (1999).
    • (1999) Inverse Probl. , vol.15 , pp. 175-187
    • Clarkson, P.A.1    Joshi, N.2    Pickering, A.3
  • 35
    • 85033968706 scopus 로고    scopus 로고
    • Higher order Painlevé equations in the polynomial class I. Bureau symbol P2
    • to be published; http://www.maths.usyd.edu.au:8000/res/Nonlinear/Cos/1998-22.html
    • C. M. Cosgrove, "Higher order Painlevé equations in the polynomial class I. Bureau symbol P2," Stud. Appl. Math, (to be published); http://www.maths.usyd.edu.au:8000/res/Nonlinear/Cos/1998-22.html
    • Stud. Appl. Math
    • Cosgrove, C.M.1
  • 36
    • 0000041709 scopus 로고    scopus 로고
    • Uniformization and transcendence of solutions for the first and second Painlevé hierarchies
    • N. A. Kudryashov and M. B. Soukharev, "Uniformization and transcendence of solutions for the first and second Painlevé hierarchies," Phys. Lett. A 237, 206-216 (1998).
    • (1998) Phys. Lett. A , vol.237 , pp. 206-216
    • Kudryashov, N.A.1    Soukharev, M.B.2
  • 37
    • 85033969607 scopus 로고    scopus 로고
    • preprint, Contact address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia
    • R. Littlewood, "Hyperelliptic asymptotics of Painlevé-type equations," preprint, 1998. (Contact address: School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia).
    • (1998) Hyperelliptic Asymptotics of Painlevé-Type Equations
    • Littlewood, R.1
  • 38
    • 44949270946 scopus 로고
    • The hénon-Heiles system revisited
    • A. P. Fordy, "The Hénon-Heiles system revisited," Physica D 52, 204-210 (1991).
    • (1991) Physica D , vol.52 , pp. 204-210
    • Fordy, A.P.1
  • 39
    • 36749119081 scopus 로고
    • Factorization of operators I. Miura transformations
    • A. P. Fordy and J. Gibbons, "Factorization of operators I. Miura transformations," J. Math. Phys. 21, 2508-2510 (1980).
    • (1980) J. Math. Phys. , vol.21 , pp. 2508-2510
    • Fordy, A.P.1    Gibbons, J.2
  • 40
    • 36749121828 scopus 로고
    • The bi-Hamiltonian structure of some nonlinear fifth-and seventh-order differential equations and recursion formulas for their symmetries and conserved covariants
    • B. Fuchssteiner and W. Oevel, "The bi-Hamiltonian structure of some nonlinear fifth-and seventh-order differential equations and recursion formulas for their symmetries and conserved covariants," J. Math. Phys. 23, 358-363 (1982).
    • (1982) J. Math. Phys. , vol.23 , pp. 358-363
    • Fuchssteiner, B.1    Oevel, W.2
  • 41
    • 0000550412 scopus 로고
    • On classes of integrable systems and the Painlevé property
    • J. Weiss, "On classes of integrable systems and the Painlevé property," J. Math. Phys. 25, 13-24 (1984).
    • (1984) J. Math. Phys. , vol.25 , pp. 13-24
    • Weiss, J.1
  • 42
    • 0021785580 scopus 로고
    • A new approach to completely integrable partial differential equations by means of the singularity analysis
    • H. Harada and S. Oishi, "A new approach to completely integrable partial differential equations by means of the singularity analysis," J. Phys. Soc. Jpn. 54, 51-56 (1985).
    • (1985) J. Phys. Soc. Jpn. , vol.54 , pp. 51-56
    • Harada, H.1    Oishi, S.2
  • 43
    • 0000531288 scopus 로고
    • An extension of nonlinear evolution equations of the KdV (mK-dV) type to higher orders
    • M. Ito, "An extension of nonlinear evolution equations of the KdV (mK-dV) type to higher orders," J. Phys. Soc. Jpn. 49, 771-778 (1980).
    • (1980) J. Phys. Soc. Jpn. , vol.49 , pp. 771-778
    • Ito, M.1
  • 45
    • 36749112076 scopus 로고
    • The Painlevé property for partial differential equations
    • J. Weiss, M. Tabor, and G. Carnevale, "The Painlevé property for partial differential equations," J. Math. Phys. 24, 522-526 (1983).
    • (1983) J. Math. Phys. , vol.24 , pp. 522-526
    • Weiss, J.1    Tabor, M.2    Carnevale, G.3
  • 46
    • 21844487106 scopus 로고
    • Factorization and Painlevé analysis of a class of nonlinear third-order partial differential equations
    • C. Gilson and A. Pickering, "Factorization and Painlevé analysis of a class of nonlinear third-order partial differential equations," J. Phys. A 28, 2871-2888 (1995).
    • (1995) J. Phys. A , vol.28 , pp. 2871-2888
    • Gilson, C.1    Pickering, A.2


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