메뉴 건너뛰기




Volumn 19, Issue 1, 2003, Pages 73-142

Algebro-geometric solutions of the Camassa-Holm hierarchy

Author keywords

Algebro geometric solutions; Camassa Holm hierarchy; Dubrovin equations; Trace formulas

Indexed keywords


EID: 0038584929     PISSN: 02132230     EISSN: 22350616     Source Type: Journal    
DOI: 10.4171/RMI/339     Document Type: Article
Times cited : (108)

References (61)
  • 1
    • 85157192093 scopus 로고    scopus 로고
    • N-component integrable systems and geometric asymptotics
    • (H. W. Braden and I. M. Krichever, editors). Gordon and Breach Science Publishers, Singapore
    • ALBER, M. S.: N-component integrable systems and geometric asymptotics. In Integrability: The Seiberg-Witten and Whitham equations (H. W. Braden and I. M. Krichever, editors). Gordon and Breach Science Publishers, Singapore, 2000, 213-228.
    • (2000) Integrability: The Seiberg-Witten and Whitham Equations , pp. 213-228
    • Alber, M.S.1
  • 3
    • 0035641135 scopus 로고    scopus 로고
    • The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDE's of shallow water and Dym type
    • ALBER, M.S., CAMASSA, R., FEDOROV, YU.N., HOLM, D.D. AND MARSDEN, J. E.: The complex geometry of weak piecewise smooth solutions of integrable nonlinear PDE's of shallow water and Dym type. Comm. Math. Phys. 221 (2001), 197-227.
    • (2001) Comm. Math. Phys. , vol.221 , pp. 197-227
    • Alber, M.S.1    Camassa, R.2    Fedorov, Yu.N.3    Holm, D.D.4    Marsden, J.E.5
  • 4
    • 0038695690 scopus 로고    scopus 로고
    • Billiard weak solutions of nonlinear PDE's and Toda flows
    • SIDE III-Symmetries and Integrability of Difference Equations (D. Levi and O. Ragnisco, editors). Amer. Math. Soc., Providence, RI
    • ALBER, M. S., CAMASSA, R. AND GEKHTMAN, M.: Billiard weak solutions of nonlinear PDE's and Toda flows. In: SIDE III-Symmetries and Integrability of Difference Equations (D. Levi and O. Ragnisco, editors). CRM Proceedings and Lecture Notes 25, 1-10. Amer. Math. Soc., Providence, RI, 2000.
    • (2000) CRM Proceedings and Lecture Notes , vol.25 , pp. 1-10
    • Alber, M.S.1    Camassa, R.2    Gekhtman, M.3
  • 5
    • 0000310316 scopus 로고
    • The geometry of peaked solitons and billiard solutions of a class of integrable PDE's
    • ALBER, M.S., CAMASSA, R., HOLM, D.D. AND MARSDEN, J.E.: The geometry of peaked solitons and billiard solutions of a class of integrable PDE's. Lett. Math. Phys. 32 (1994), 137-151.
    • (1994) Lett. Math. Phys. , vol.32 , pp. 137-151
    • Alber, M.S.1    Camassa, R.2    Holm, D.D.3    Marsden, J.E.4
  • 6
    • 0000960226 scopus 로고
    • On the link between umbilic geodesics and soliton solutions of nonlinear PDE's
    • ALBER, M.S., CAMASSA, R., HOLM, D.D. AND MARSDEN, J.E.: On the link between umbilic geodesics and soliton solutions of nonlinear PDE's. Proc. Roy. Soc. London Ser. A 450 (1995), 677-692.
    • (1995) Proc. Roy. Soc. London Ser. A , vol.450 , pp. 677-692
    • Alber, M.S.1    Camassa, R.2    Holm, D.D.3    Marsden, J.E.4
  • 7
    • 0034367365 scopus 로고    scopus 로고
    • Wave solutions of evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians
    • ALBER, M.S. AND FEDOROV, YU. N.: Wave solutions of evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians. J. Phys. A 33 (2000), 8409-8425.
    • (2000) J. Phys. A , vol.33 , pp. 8409-8425
    • Alber, M.S.1    Fedorov, Yu.N.2
  • 8
    • 0035420587 scopus 로고    scopus 로고
    • Algebraic geometrical solutions for certain evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians
    • ALBER, M. S. AND FEDOROV, YU. N.: Algebraic geometrical solutions for certain evolution equations and Hamiltonian flows on nonlinear subvarieties of generalized Jacobians. Inverse Problems 17 (2001), 1017-1042.
    • (2001) Inverse Problems , vol.17 , pp. 1017-1042
    • Alber, M.S.1    Fedorov, Yu.N.2
  • 9
    • 0033632359 scopus 로고    scopus 로고
    • On soliton-type solutions of equations associated with N-component systems
    • ALBER, M. S., LUTHER, G. G. AND MILLER, C. A.: On soliton-type solutions of equations associated with N-component systems. J. Math. Phys. 41 (2000), 284-316.
    • (2000) J. Math. Phys. , vol.41 , pp. 284-316
    • Alber, M.S.1    Luther, G.G.2    Miller, C.A.3
  • 10
    • 0038019338 scopus 로고    scopus 로고
    • Peakon solitons of the shallow water equation
    • ALBER, M. S. AND MILLER, C.: Peakon solitons of the shallow water equation. Appl. Math. Lett 14 (2001), 93-98.
    • (2001) Appl. Math. Lett. , vol.14 , pp. 93-98
    • Alber, M.S.1    Miller, C.2
  • 11
    • 0000174121 scopus 로고    scopus 로고
    • Acoustic scattering and the extended Korteweg-de Vries hierarchy
    • BEALS, R., SATTINGER, D.H. AND SZMIGIELSKI, J.: Acoustic scattering and the extended Korteweg-de Vries hierarchy. Adv. Math. 140 (1998), 190-206.
    • (1998) Adv. Math. , vol.140 , pp. 190-206
    • Beals, R.1    Sattinger, D.H.2    Szmigielski, J.3
  • 13
    • 0034714658 scopus 로고    scopus 로고
    • Multipeakons and the classical moment problem
    • BEALS, R., SATTINGER, D. H. AND SZMIGIELSKI, J.: Multipeakons and the classical moment problem. Adv. in Math. 154 (2000), 229-257.
    • (2000) Adv. in Math. , vol.154 , pp. 229-257
    • Beals, R.1    Sattinger, D.H.2    Szmigielski, J.3
  • 16
    • 0032162250 scopus 로고    scopus 로고
    • Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchy
    • BULLA, W., GESZTESY, F., HOLDEN, H. AND TESCHL, G.: Algebro-geometric quasi-periodic finite-gap solutions of the Toda and Kac-van Moerbeke hierarchy. Mem. Amer. Math. Soc. 135 (1998), no. 641, 1-79.
    • (1998) Mem. Amer. Math. Soc. , vol.135 , Issue.641 , pp. 1-79
    • Bulla, W.1    Gesztesy, F.2    Holden, H.3    Teschl, G.4
  • 17
    • 12044254491 scopus 로고
    • An integrable shallow water equation with peaked solitons
    • CAMASSA, R. AND HOLM, D. D.: An integrable shallow water equation with peaked solitons. Phys. Rev. Lett. 71 (1993), 1661-1664.
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 1661-1664
    • Camassa, R.1    Holm, D.D.2
  • 18
    • 56349110516 scopus 로고
    • A new integrable shallow water equation
    • CAMASSA, R., HOLM, D. D. AND HYMAN, J. M.: A new integrable shallow water equation. Adv. Appl. Mech. 31 (1994), 1-33.
    • (1994) Adv. Appl. Mech. , vol.31 , pp. 1-33
    • Camassa, R.1    Holm, D.D.2    Hyman, J.M.3
  • 20
    • 0000213450 scopus 로고    scopus 로고
    • On the Cauchy problem for the periodic Camassa-Holm equation
    • CONSTANTIN, A.: On the Cauchy problem for the periodic Camassa-Holm equation. J. Differential Equations 141 (1997), 218-235.
    • (1997) J. Differential Equations , vol.141 , pp. 218-235
    • Constantin, A.1
  • 21
    • 0000684999 scopus 로고    scopus 로고
    • On the inverse spectral problem for the Camassa-Holm equation
    • CONSTANTIN, A.: On the inverse spectral problem for the Camassa-Holm equation. J. Funct. Anal. 155 (1998), 352-363.
    • (1998) J. Funct. Anal. , vol.155 , pp. 352-363
    • Constantin, A.1
  • 22
    • 0032210147 scopus 로고    scopus 로고
    • Quasi-periodicity with respect to time of spatially periodic finite-gap solutions of the Camassa-Holm equation
    • CONSTANTIN, A.: Quasi-periodicity with respect to time of spatially periodic finite-gap solutions of the Camassa-Holm equation. Bull. Sci. Math. 122 (1998), 487-494.
    • (1998) Bull. Sci. Math. , vol.122 , pp. 487-494
    • Constantin, A.1
  • 23
    • 0034415062 scopus 로고    scopus 로고
    • Existence of permanent and breaking waves for a shallow water equation: A geometric approach
    • CONSTANTIN, A.: Existence of permanent and breaking waves for a shallow water equation: a geometric approach. Ann. Inst. Fourier (Grenoble) 50 (2000), 321-362.
    • (2000) Ann. Inst. Fourier (Grenoble) , vol.50 , pp. 321-362
    • Constantin, A.1
  • 25
    • 0000468550 scopus 로고    scopus 로고
    • Global weak solutions for a shallow water equation
    • CONSTANTIN, A. AND ESCHER, J.: Global weak solutions for a shallow water equation. Indiana Univ. Math. J. 47 (1998), 1527-1545.
    • (1998) Indiana Univ. Math. J. , vol.47 , pp. 1527-1545
    • Constantin, A.1    Escher, J.2
  • 26
    • 0000985293 scopus 로고    scopus 로고
    • Wave breaking for nonlinear nonlocal shallow water equations
    • CONSTANTIN, A. AND ESCHER, J.: Wave breaking for nonlinear nonlocal shallow water equations. Acta Math. 181 (1998), 229-243.
    • (1998) Acta Math. , vol.181 , pp. 229-243
    • Constantin, A.1    Escher, J.2
  • 27
    • 0032374820 scopus 로고    scopus 로고
    • Well-posedness, global existence, and blow-up phenomena for a periodic quasi-linear hyperbolic equation
    • CONSTANTIN, A. AND ESCHER, J.: Well-posedness, global existence, and blow-up phenomena for a periodic quasi-linear hyperbolic equation. Comm. Pure Appl. Math. 51 (1998), 475-504.
    • (1998) Comm. Pure Appl. Math. , vol.51 , pp. 475-504
    • Constantin, A.1    Escher, J.2
  • 28
    • 0034347295 scopus 로고    scopus 로고
    • On the blow-up rate and the blow-up set of breaking waves for a shallow water equation
    • CONSTANTIN, A. AND ESCHER, J.: On the blow-up rate and the blow-up set of breaking waves for a shallow water equation. Math. Z. 233 (2000), 75-91.
    • (2000) Math. Z. , vol.233 , pp. 75-91
    • Constantin, A.1    Escher, J.2
  • 29
    • 0033415933 scopus 로고    scopus 로고
    • A shallow water equation on the circle
    • CONSTANTIN, A. AND MCKEAN, H. P.: A shallow water equation on the circle. Comm. Pure Appl. Math. 52 (1999), 949-982.
    • (1999) Comm. Pure Appl. Math. , vol.52 , pp. 949-982
    • Constantin, A.1    McKean, H.P.2
  • 30
    • 0034349440 scopus 로고    scopus 로고
    • Global weak solutions for a shallow water equation
    • CONSTANTIN, A. AND MOLINET, L.: Global weak solutions for a shallow water equation. Comm. Math. Phys. 211 (2000), 45-61.
    • (2000) Comm. Math. Phys. , vol.211 , pp. 45-61
    • Constantin, A.1    Molinet, L.2
  • 31
    • 0010085710 scopus 로고    scopus 로고
    • Algebro-geometric solutions of the Boussinesq hierarchy
    • DICKSON, R., GESZTESY, F. AND UNTERKOFLER, K.: Algebro-geometric solutions of the Boussinesq hierarchy. Rev. Math. Phys. 11 (1999), 823-879.
    • (1999) Rev. Math. Phys. , vol.11 , pp. 823-879
    • Dickson, R.1    Gesztesy, F.2    Unterkofler, K.3
  • 32
    • 0001776511 scopus 로고    scopus 로고
    • A new approach to the Boussinesq hierarchy
    • DICKSON, R., GESZTESY, F. AND UNTERKOFLER, K.: A new approach to the Boussinesq hierarchy. Math. Nachr. 198 (1999), 51-108.
    • (1999) Math. Nachr. , vol.198 , pp. 51-108
    • Dickson, R.1    Gesztesy, F.2    Unterkofler, K.3
  • 33
    • 0010979902 scopus 로고
    • Finite-gap solutions of the Harry Dym equation
    • DMITRIEVA, L. A.: Finite-gap solutions of the Harry Dym equation. Phys. Lett. A 182 (1993), 65-70.
    • (1993) Phys. Lett. A , vol.182 , pp. 65-70
    • Dmitrieva, L.A.1
  • 34
    • 40749103220 scopus 로고    scopus 로고
    • An integrable shallow water equation with linear and nonlinear dispersion
    • DULLIN, H.R., GOTTWALD, G. AND HOLM, D.D.: An integrable shallow water equation with linear and nonlinear dispersion. Phys. Rev. Lett. 87 (2001), 4501-4504.
    • (2001) Phys. Rev. Lett. , vol.87 , pp. 4501-4504
    • Dullin, H.R.1    Gottwald, G.2    Holm, D.D.3
  • 35
    • 0038019337 scopus 로고    scopus 로고
    • The classical massive thirring system revisited
    • Stochastic Processes, Physics and Geometry: New Interplays. I: A Volume in Honor of Sergio Albeverio (F. Gesztesy, H. Holden, J. Jost, S. Paycha, M. Röckner, and S. Scarlatti, editors). Amer. Math. Soc., Providence, RI
    • ENOLSKII, V. Z., GESZTESY, F. AND HOLDEN, H.: The classical massive Thirring system revisited. In: Stochastic Processes, Physics and Geometry: New Interplays. I: A Volume in Honor of Sergio Albeverio (F. Gesztesy, H. Holden, J. Jost, S. Paycha, M. Röckner, and S. Scarlatti, editors). CMS Conference Proceedings 28, Amer. Math. Soc., Providence, RI, 2000, 163-200.
    • (2000) CMS Conference Proceedings , vol.28 , pp. 163-200
    • Enolskii, V.Z.1    Gesztesy, F.2    Holden, H.3
  • 37
    • 0042877956 scopus 로고    scopus 로고
    • Classical integrable systems and billiards related to generalized Jacobians
    • FEDOROV, YU.: Classical integrable systems and billiards related to generalized Jacobians. Acta. Appl. Math. 55 (1999), 251-301.
    • (1999) Acta. Appl. Math. , vol.55 , pp. 251-301
    • Fedorov, Yu.1
  • 38
    • 0001500560 scopus 로고    scopus 로고
    • The Camassa Holm equation: Conserved quantities and the initial value problem
    • FISHER, M. AND SCHIFF, J.: The Camassa Holm equation: conserved quantities and the initial value problem. Phys. Lett. A 259 (1999), 371-376.
    • (1999) Phys. Lett. A , vol.259 , pp. 371-376
    • Fisher, M.1    Schiff, J.2
  • 39
    • 36749037534 scopus 로고    scopus 로고
    • The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory
    • FOIAS, C., HOLM, D.D. AND TITI, E. S.: The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory. J. Dynam. Diff. Eq. 14 (2002), 1-35.
    • (2002) J. Dynam. Diff. Eq. , vol.14 , pp. 1-35
    • Foias, C.1    Holm, D.D.2    Titi, E.S.3
  • 40
    • 0017901962 scopus 로고
    • A numerical and theoretical study of certain nonlinear wave phenomena
    • FORNBERG, B. AND WITHAM, G. B.: A numerical and theoretical study of certain nonlinear wave phenomena. Philos. Trans. Roy. Soc. London Ser. A 289 (1978), 373-404.
    • (1978) Philos. Trans. Roy. Soc. London Ser. A , vol.289 , pp. 373-404
    • Fornberg, B.1    Witham, G.B.2
  • 41
    • 22244482803 scopus 로고    scopus 로고
    • Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
    • FUCHSSTEINER, B.: Some tricks from the symmetry-toolbox for nonlinear equations: generalizations of the Camassa-Holm equation. Phys. D 95 (1996), 229-243.
    • (1996) Phys. D , vol.95 , pp. 229-243
    • Fuchssteiner, B.1
  • 42
    • 49049150360 scopus 로고
    • Symplectic structures, their Bäcklund transformations and hereditary symmetries
    • FUCHSSTEINER, B. AND FOKAS, A. S.: Symplectic structures, their Bäcklund transformations and hereditary symmetries. Phys. D 4 (1981), 47-66.
    • (1981) Phys. D , vol.4 , pp. 47-66
    • Fuchssteiner, B.1    Fokas, A.S.2
  • 43
    • 35848937240 scopus 로고
    • Abelian integrals and the reduction method for an integrable Hamiltonian system
    • GAGNON, L., HARNAD, J., WINTERNITZ, P. AND HURTUBISE, J.: Abelian integrals and the reduction method for an integrable Hamiltonian system. J. Math. Phys. 26 (1985), 1605-1612.
    • (1985) J. Math. Phys. , vol.26 , pp. 1605-1612
    • Gagnon, L.1    Harnad, J.2    Winternitz, P.3    Hurtubise, J.4
  • 44
    • 0033416562 scopus 로고    scopus 로고
    • Generalized Jacobians of spectral curves and completely integrable systems
    • GAVRILOV, L.: Generalized Jacobians of spectral curves and completely integrable systems. Math. Z. 230 (1999), 487-508.
    • (1999) Math. Z. , vol.230 , pp. 487-508
    • Gavrilov, L.1
  • 45
    • 0036402991 scopus 로고    scopus 로고
    • Dubrovin equations and integrable systems on hyperelliptic curves
    • GESZTESY, F. AND HOLDEN, H.: Dubrovin equations and integrable systems on hyperelliptic curves. Math. Scand. 91 (2002), 91-126.
    • (2002) Math. Scand. , vol.91 , pp. 91-126
    • Gesztesy, F.1    Holden, H.2
  • 47
    • 79961210956 scopus 로고    scopus 로고
    • A combined sine-Gordon and modified Korteweg-de Vries hierarchy and its algebro-geometric solutions
    • Differential Equations and Mathematical Physics (R. Weikard and G. Weinstein, editors), Amer. Math. Soc. and International Press, Providence and Boston
    • GESZTESY, F. AND HOLDEN, H.: A combined sine-Gordon and modified Korteweg-de Vries hierarchy and its algebro-geometric solutions. In: Differential Equations and Mathematical Physics (R. Weikard and G. Weinstein, editors), 133-173. Studies in Advanced Mathematics 16, Amer. Math. Soc. and International Press, Providence and Boston, 2000.
    • (2000) Studies in Advanced Mathematics , vol.16 , pp. 133-173
    • Gesztesy, F.1    Holden, H.2
  • 48
    • 0034359009 scopus 로고    scopus 로고
    • Darboux-type transformations and hyperelliptic curves
    • GESZTESY, F. AND HOLDEN, H.: Darboux-type transformations and hyperelliptic curves. J. Reine Angew. Math. 527 (2000), 151-183.
    • (2000) J. Reine Angew. Math. , vol.527 , pp. 151-183
    • Gesztesy, F.1    Holden, H.2
  • 49
    • 0032222021 scopus 로고    scopus 로고
    • An alternative approach to algebro-geometric solutions of the AKNS hierarchy
    • GESZTESY, F. AND RATNASEELAN, R.: An alternative approach to algebro-geometric solutions of the AKNS hierarchy. Rev. Math. Phys. 10 (1998), 345-391.
    • (1998) Rev. Math. Phys. , vol.10 , pp. 345-391
    • Gesztesy, F.1    Ratnaseelan, R.2
  • 50
    • 0001124817 scopus 로고    scopus 로고
    • The KdV hierarchy and associated trace formulas
    • Recent Developments in Operator Theory and Its Applications (I. Gohberg, P. Lancaster, and P.N. Shivakumar, editors). Birkhäuser, Basel
    • GESZTESY, F., RATNASEELAN, R. AND TESCHL, G.: The KdV hierarchy and associated trace formulas. In: Recent Developments in Operator Theory and Its Applications (I. Gohberg, P. Lancaster, and P.N. Shivakumar, editors). Operator Theory: Advances and Applications 87, Birkhäuser, Basel, (1996), 125-163.
    • (1996) Operator Theory: Advances and Applications , vol.87 , pp. 125-163
    • Gesztesy, F.1    Ratnaseelan, R.2    Teschl, G.3
  • 51
    • 0037171407 scopus 로고    scopus 로고
    • Camassa-Holm, Korteweg-de Vries and related models for water waves
    • JOHNSON, R. S.: Camassa-Holm, Korteweg-de Vries and related models for water waves. J. Fluid Mech. 455 (2002), 63-82.
    • (2002) J. Fluid Mech. , vol.455 , pp. 63-82
    • Johnson, R.S.1
  • 52
    • 0034407954 scopus 로고    scopus 로고
    • The geometry and analysis of the averaged Euler equations and a new diffeomorphism group
    • MARSDEN, J.E., RATIU, T. S. AND SHKOLLER, S.: The geometry and analysis of the averaged Euler equations and a new diffeomorphism group. Geom. Funct. Anal 10 (2000), 582-599.
    • (2000) Geom. Funct. Anal , vol.10 , pp. 582-599
    • Marsden, J.E.1    Ratiu, T.S.2    Shkoller, S.3
  • 53
    • 0038111248 scopus 로고    scopus 로고
    • Global well-posedness for the Lagrangian averaged Navier-Stokes (LANS-α) equations on bounded domains
    • MARSDEN, J. E. AND SHKOLLER, S.: Global well-posedness for the Lagrangian averaged Navier-Stokes (LANS-α) equations on bounded domains. R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci. 359 (2001), 1449-1468.
    • (2001) R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci. , vol.359 , pp. 1449-1468
    • Marsden, J.E.1    Shkoller, S.2
  • 54
    • 0031989845 scopus 로고    scopus 로고
    • A shallow water equation as a geodesic flow on the Bott-Virasoro group
    • MISIOLEK, G.: A shallow water equation as a geodesic flow on the Bott-Virasoro group. J. Geom. Phys. 24 (1998), 203-208.
    • (1998) J. Geom. Phys. , vol.24 , pp. 203-208
    • Misiolek, G.1
  • 55
    • 0003358349 scopus 로고
    • Tata lectures on theta II
    • Birkhäuser, Boston
    • MUMFORD, D.: Tata Lectures on Theta II. Progress in Mathematics 43, Birkhäuser, Boston, 1984.
    • (1984) Progress in Mathematics , vol.43
    • Mumford, D.1
  • 56
    • 0010573520 scopus 로고    scopus 로고
    • Algebraic-geometric solutions of the Harry Dym equation
    • NOVIKOV, D. P.: Algebraic-geometric solutions of the Harry Dym equation. Siberian Math. J. 40 (1999), 136-140.
    • (1999) Siberian Math. J. , vol.40 , pp. 136-140
    • Novikov, D.P.1
  • 57
    • 0030544208 scopus 로고    scopus 로고
    • Zero curvature formulations of dual hierarchies
    • SCHIFF, J.: Zero curvature formulations of dual hierarchies. J. Math. Phys. 37 (1996), 1928-1938.
    • (1996) J. Math. Phys. , vol.37 , pp. 1928-1938
    • Schiff, J.1
  • 58
    • 0002936313 scopus 로고    scopus 로고
    • 1 metric and mean hydrodynamics
    • 1 metric and mean hydrodynamics. J. Funct. Anal. 160 (1998), 337-365.
    • (1998) J. Funct. Anal. , vol.160 , pp. 337-365
    • Shkoller, S.1
  • 60
    • 0003805793 scopus 로고
    • Theory of nonlinear lattices, second edition
    • Springer, Berlin
    • TODA, M.: Theory of Nonlinear Lattices, second edition. Solid-State Sciences 20, Springer, Berlin, 1989.
    • (1989) Solid-State Sciences , vol.20
    • Toda, M.1
  • 61
    • 0034394008 scopus 로고    scopus 로고
    • On the weak solutions to a shallow water equation
    • XIN, Z. AND ZHANG, P.: On the weak solutions to a shallow water equation. Comm. Pure Appl. Math. 53 (2000), 1411-1433.
    • (2000) Comm. Pure Appl. Math. , vol.53 , pp. 1411-1433
    • Xin, Z.1    Zhang, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.