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Volumn 34, Issue 6, 2003, Pages 1253-1278

On the discrete spectrum of systems in the plane and the Davey-Stewartson II equation

Author keywords

Integrable equations; Interacting solitons; Spectral analysis

Indexed keywords


EID: 0242511217     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141001391627     Document Type: Article
Times cited : (18)

References (24)
  • 1
    • 0000541374 scopus 로고
    • On three-dimensional packets of surface waves
    • A. DAVEY AND K. STEWARTSON, On three-dimensional packets of surface waves, Proc. Roy. Soc. London Ser. A, 338 (1974), pp. 101-110.
    • (1974) Proc. Roy. Soc. London Ser. A , vol.338 , pp. 101-110
    • Davey, A.1    Stewartson, K.2
  • 2
    • 0018480221 scopus 로고
    • On the evolution of packets of water waves
    • M. J. ABLOWITZ AND H. SEGUR, On the evolution of packets of water waves, J. Fluid Mech., 92 (1979), pp. 691-715.
    • (1979) J. Fluid Mech. , vol.92 , pp. 691-715
    • Ablowitz, M.J.1    Segur, H.2
  • 4
    • 0001517738 scopus 로고
    • Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation
    • V. A. ARKADIEV, A. K. PROGREBKOV, AND M. C. POLIVANOV, Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation, Phys. D, 36 (1989), pp. 189-197.
    • (1989) Phys. D , vol.36 , pp. 189-197
    • Arkadiev, V.A.1    Progrebkov, A.K.2    Polivanov, M.C.3
  • 5
    • 0002004721 scopus 로고
    • Solitons, Nonlinear Evolution Equations and Inverse Scattering
    • Cambridge University Press, Cambridge, UK
    • M. J. ABLOWITZ AND P. A. CLARKSON, Solitons, Nonlinear Evolution Equations and Inverse Scattering, London Math. Soc. Lecture Note Ser. 149, Cambridge University Press, Cambridge, UK, 1989.
    • (1989) London Math. Soc. Lecture Note Ser. , vol.149
    • Ablowitz, M.J.1    Clarkson, P.A.2
  • 6
    • 0242503534 scopus 로고
    • Comments on the inverse scattering transform and related nonlinear evolution equations
    • Nonlinear Phenomena (Oaxtepec, 1982), Springer-Verlag, Berlin. See also [7].
    • M. J. ABLOWITZ AND A. S. FOKAS, Comments on the inverse scattering transform and related nonlinear evolution equations, in Nonlinear Phenomena (Oaxtepec, 1982), Lecture Notes in Phys. 189, Springer-Verlag, Berlin, 1983, pp. 3-24. See also [7].
    • (1983) Lecture Notes in Phys. , vol.189 , pp. 3-24
    • Ablowitz, M.J.1    Fokas, A.S.2
  • 7
    • 0041822401 scopus 로고
    • The inverse scattering transform for multidimensional (2 + 1) problems
    • in Nonlinear Phenomena (Oaxtepec, 1982), Springer-Verlag, Berlin
    • A. S. FOKAS AND M. J. ABLOWITZ, The inverse scattering transform for multidimensional (2 + 1) problems, in Nonlinear Phenomena (Oaxtepec, 1982), Lecture Notes in Phys. 189, Springer-Verlag, Berlin, 1983, pp. 137-183.
    • (1983) Lecture Notes in Phys. , vol.189 , pp. 137-183
    • Fokas, A.S.1    Ablowitz, M.J.2
  • 8
    • 0001465096 scopus 로고
    • On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane
    • A. FOKAS AND M. J. ABLOWITZ, On the inverse scattering transform of multidimensional nonlinear equations related to first-order systems in the plane, J. Math. Phys., 25 (1984), pp. 2494-2505.
    • (1984) J. Math. Phys. , vol.25 , pp. 2494-2505
    • Fokas, A.1    Ablowitz, M.J.2
  • 9
    • 0026172481 scopus 로고
    • On the Hamiltonian formalism for the Davey-Stewartson system
    • J. VILLARROEL AND M. J. ABLOWITZ, On the Hamiltonian formalism for the Davey-Stewartson system, Inverse Problems, 7 (1991), pp. 451-460.
    • (1991) Inverse Problems , vol.7 , pp. 451-460
    • Villarroel, J.1    Ablowitz, M.J.2
  • 10
    • 0242672032 scopus 로고
    • On the complete integrability of certain nonlinear evolution equations in one and two spatial dimensions
    • (Canberra), World Scientific, Teaneck, NJ
    • M. J. ABLOWITZ AND J. VILLARROEL, On the complete integrability of certain nonlinear evolution equations in one and two spatial dimensions, in Chaos & Order (Canberra, 1990), World Scientific, Teaneck, NJ, 1991, pp. 1-13.
    • (1990) Chaos & Order , pp. 1-13
    • Ablowitz, M.J.1    Villarroel, J.2
  • 11
    • 0001294784 scopus 로고    scopus 로고
    • Solutions to the time dependent Schrödinger and the Kadomtsev-Petviashvili equations
    • M. J. ABLOWITZ AND J. VILLARROEL, Solutions to the time dependent Schrödinger and the Kadomtsev-Petviashvili equations, Phys. Rev. Lett., 78 (1997), pp. 570-573.
    • (1997) Phys. Rev. Lett. , vol.78 , pp. 570-573
    • Ablowitz, M.J.1    Villarroel, J.2
  • 12
    • 0033216639 scopus 로고    scopus 로고
    • On the discrete spectrum of the nonstationary Schrödinger equation and multipole lumps of the Kadomtsev-Petviashvili I equation
    • J. VILLARROEL AND M. J. ABLOWITZ, On the discrete spectrum of the nonstationary Schrödinger equation and multipole lumps of the Kadomtsev-Petviashvili I equation, Comm. Math. Phys., 207 (1999), pp. 1-42.
    • (1999) Comm. Math. Phys. , vol.207 , pp. 1-42
    • Villarroel, J.1    Ablowitz, M.J.2
  • 13
    • 0042228757 scopus 로고    scopus 로고
    • Solutions of the Davey-Stewartson II equation with arbitrary rational localization and nontrivial interaction
    • M. MAÑAS AND P. SANTINI, Solutions of the Davey-Stewartson II equation with arbitrary rational localization and nontrivial interaction, Phys. Lett. A, 227 (1997), pp. 325-334.
    • (1997) Phys. Lett. A , vol.227 , pp. 325-334
    • Mañas, M.1    Santini, P.2
  • 14
    • 33744738036 scopus 로고
    • Nontrivial scattering of localized solitons in a (2 + 1)-dimensional integrable system
    • R. S. WARD, Nontrivial scattering of localized solitons in a (2 + 1)-dimensional integrable system, Phys. Lett. A, 208 (1995), pp. 203-208.
    • (1995) Phys. Lett. A , vol.208 , pp. 203-208
    • Ward, R.S.1
  • 15
    • 0000756659 scopus 로고
    • Normal and anomalous scattering, formation and decay of bound states of two-dimensional solitons described by the Kadomtsev-Petviashvili equation
    • K. A. GORSHKOV, D. E. PELINOVSKY, AND Yu. A. STEPANYANTS, Normal and anomalous scattering, formation and decay of bound states of two-dimensional solitons described by the Kadomtsev-Petviashvili equation, JETP, 77 (1993), pp. 237-245.
    • (1993) JETP , vol.77 , pp. 237-245
    • Gorshkov, K.A.1    Pelinovsky, D.E.2    Stepanyants, Yu.A.3
  • 16
    • 0034642817 scopus 로고    scopus 로고
    • A novel class of solutions of the non-stationary Schrödinger and the Kadomtsev-Petviashvili I equations
    • M. J. ABLOWITZ, S. CHAKRAVARTY, A. D. TRUBATCH, AND J. VILLARROEL, A novel class of solutions of the non-stationary Schrödinger and the Kadomtsev-Petviashvili 1 equations, Phys. Lett. A, 267 (2000), pp. 132-146.
    • (2000) Phys. Lett. A , vol.267 , pp. 132-146
    • Ablowitz, M.J.1    Chakravarty, S.2    Trubatch, A.D.3    Villarroel, J.4
  • 17
    • 0032356665 scopus 로고    scopus 로고
    • Rational solutions of the KP hierarchy and the dynamics of their poles. II. Construction of the degenerate polynomial solutions
    • D. PELINOVSKY, Rational solutions of the KP hierarchy and the dynamics of their poles. II. Construction of the degenerate polynomial solutions, J. Math. Phys., 39 (1998), pp. 5377-5395.
    • (1998) J. Math. Phys. , vol.39 , pp. 5377-5395
    • Pelinovsky, D.1
  • 18
    • 0007743266 scopus 로고    scopus 로고
    • Vectorial Darboux transformations for the Kadomtsev-Petviashvili hierarchy
    • Q. P. LIU AND M. MAÑAS, Vectorial Darboux transformations for the Kadomtsev-Petviashvili hierarchy, J. Nonlinear Sci., 9 (1999), pp. 213-232.
    • (1999) J. Nonlinear Sci. , vol.9 , pp. 213-232
    • Liu, Q.P.1    Mañas, M.2
  • 19
    • 0001605032 scopus 로고
    • On the solvability of the N-wave, Davey-Stewartson and Kadomtsev-Petviashvili equations
    • A. S. FOKAS AND L.-Y. SUNG, On the solvability of the N-wave, Davey-Stewartson and Kadomtsev-Petviashvili equations, Inverse Problems, 8 (1992), pp. 673-708.
    • (1992) Inverse Problems , vol.8 , pp. 673-708
    • Fokas, A.S.1    Sung, L.-Y.2
  • 20
    • 38149146155 scopus 로고
    • An inverse scattering transform for the Davey-Stewartson II equations. I
    • L.-Y. SUNG, An inverse scattering transform for the Davey-Stewartson II equations. I, J. Math. Anal. Appl., 183 (1994), pp. 121-154.
    • (1994) J. Math. Anal. Appl. , vol.183 , pp. 121-154
    • Sung, L.-Y.1
  • 21
    • 38149148161 scopus 로고
    • An inverse scattering transform for the Davey-Stewartson II equations. II
    • L.-Y. SUNG, An inverse scattering transform for the Davey-Stewartson II equations. II, J. Math. Anal. Appl., 183 (1994), pp. 289-325.
    • (1994) J. Math. Anal. Appl. , vol.183 , pp. 289-325
    • Sung, L.-Y.1
  • 22
    • 38149147423 scopus 로고
    • An inverse scattering transform for the Davey-Stewartson II equations. III
    • L.-Y. SUNG, An inverse scattering transform for the Davey-Stewartson II equations. III, J. Math. Anal. Appl., 183 (1994), pp. 477-494.
    • (1994) J. Math. Anal. Appl. , vol.183 , pp. 477-494
    • Sung, L.-Y.1
  • 23
    • 0009399073 scopus 로고    scopus 로고
    • Spectral decomposition for the Dirac system associated to the DSII equation
    • D. E. PELINOVSKY AND C. SULEM, Spectral decomposition for the Dirac system associated to the DSII equation, Inverse Problems, 16 (2000), pp. 59-74.
    • (2000) Inverse Problems , vol.16 , pp. 59-74
    • Pelinovsky, D.E.1    Sulem, C.2


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