Inverse scattering transform for the integrable discrete nonlinear Schrödinger equation with nonvanishing boundary conditions

Inverse Problems

Volumn 23, Issue 4, 2007, Pages 1711-1758

  Ablowitz, Mark J ^a   Biondini, Gino ^b   Prinari, Barbara ^c  

^a UNIVERSITY OF COLORADO   (United States)

^b UNIVERSITY AT BUFFALO   (United States)

^c UNIVERSITY OF SALENTO   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; NONLINEAR SYSTEMS; SOLITONS;

DINGER EQUATION; INVERSE SCATTERING TRANSFORM; SOLITON SOLUTIONS;

INVERSE PROBLEMS;

EID: 34548662164     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/23/4/021     Document Type: Article

References (25)

1. Zakharov V E and Shabat A B 1972 Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of wave in nonlinear media Sov. Phys.-JETP 34 62-9
2. Zakharov V E and Shabat A B 1973 Interaction between solitons in a stable medium Sov. Phys.-JETP 37 823-8
3. Kulish P P, Manakov S V and Fadeev L D 1976 Comparison of the exact quantum and quasiclassical results for a nonlinear Schrödinger equation Theor. Math. Phys. 28 625
4. Kawata T and Inoue H 1977 Eigen value problem with nonvanishing potentials J. Phys. Soc. Japan. Lett. 43 361-2
5. Kawata T and Inoue H 1978 Inverse scattering method for nonlinear evolution equations under nonvanishing conditions J. Phys. Soc. Japan 44 1722-9
6. Asano N and Kato Y 1981 Non-self-adjoint Zakharov-Shabat operator with a potential of the finite asymptotic values: I. Direct spectral and scattering problems J. Math. Phys. 22 2780
7. Asano N and Kato Y 1984 Non-self-adjoint Zakharov-Shabat operator with a potential of the finite asymptotic values: I. Direct spectral and scattering problems J. Math. Phys. 25 570
8. Gerdjikov V S and Kulish P P 1978 Completely integrable Hamiltonian systems connected with the non self-adjoint Dirac operator Bulg. J. Phys. 5 337 (in Russian)
9. Leon J 1980 The Dirac inverse spectral transform: kinks and boomerons J. Math. Phys. 21 2572
10. Boiti M and Pempinelli F 1982 The spectral transform for the NLS equation with left-right asymmetric boundary conditions Nuovo Cimento 69 213
11. Faddeev L D and Takhtajan L A 1987 Hamiltonian Methods in the Theory of Solitons (Berlin: Springer)
12. Kivshar Y S and Luther-Davies B 1998 Dark optical solitons: physics and applications Phys. Rep. 298 81
13. Prinari B, Ablowitz M J and Biondini G 2006 Inverse scattering transform for vector nonlinear Schrödinger equation with non-vanishing boundary conditions J. Math. Phys. 47 063508
14. Ieda J-i, Uchiyama M and Wadati M 2007 Inverse scattering method for square matrix nonlinear Schrödinger equation under nonvanishing boundary conditions J. Math. Phys. 48 013507
15. Ablowitz M J and Ladik J F 1975 Nonlinear differential-difference equations J. Math. Phys. 16 598-603
16. Ablowitz M J and Ladik J F 1976 Nonlinear differential-difference equations and Fourier analysis J. Math. Phys. 17 1011-8
17. Ablowitz M J, Prinari B and Trubatch A D 2004 Discrete and Continuous Nonlinear Schrödinger Systems (Cambridge: Cambridge University Press)
18. Takeno S and Hori K 1990 A propagating self-localized mode in a one-dimensional lattice with quartic anharmonicity J. Phys. Soc. Japan 59 3037-40
19. Kenkre V M and Campbell D K 1986 Self-trapping on a dimer: time-dependent solutions of a discrete nonlinear Schrödinger equation Phys. Rev. B 34 4959-61
20. Ishimori Y 1982 An integrable classical spin chain J. Phys. Soc. Japan 51 3417-8
21. Papanicoulau N 1987 Complete integrability for a discrete Heisenberg chain J. Phys. A: Math. Gen. 20 3637-52
22. Vekslerchik V E and Konotop V V 1992 Discrete nonlinear Schrödinger equation under non-vanishing boundary conditions Inverse Problems 8 889-909
23. Kulish P P 1981 Quantum difference nonlinear Schrödinger equation Latt. Math. Phys. 5 191-7
24. Konotop V V and Vekslerchik V E 1992 On soliton creation in the nonlinear Schrödinger model. Discrete and continuous versions J. Phys. A: Math. Gen. 25 4037-42
25. Maruno K-i and Ohta Y 2006 Casorati determinant form of dark soliton solutions of the discrete nonlinear Schrödinger equation J. Phys. Soc. Japan 75 054002