Inverse scattering method for square matrix nonlinear Schrödinger equation under nonvanishing boundary conditions

DOI10.1063/1.2423222zbMath1121.37057arXivnlin/0603010OpenAlexW3124328519MaRDI QIDQ3442182

Jun'ichi Ieda, Miki Wadati, Masaru Uchiyama

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0603010

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Inverse problems involving ordinary differential equations (34A55) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (8)

Riemann-Hilbert approach to TD equation with nonzero boundary condition ⋮ Inverse scattering problem for the matrix modified Korteweg-de Vries equation with finite density type initial data ⋮ Inverse scattering transform for nonlinear Schrödinger systems on a nontrivial background: a survey of classical results, new developments and future directions ⋮ Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions ⋮ Riemann-Hilbert problem for the modified Landau-Lifshitz equation with nonzero boundary conditions ⋮ Painlevé singularity structure analysis of three component Gross–Pitaevskii type equations ⋮ Reflectionless solutions for square matrix NLS with vanishing boundary conditions ⋮ Inverse Scattering Transform and Solitons for Square Matrix Nonlinear Schrödinger Equations with Mixed Sign Reductions and Nonzero Boundary Conditions

Cites Work

• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• The Coupled Modified Korteweg-de Vries Equations
• Relationships among Inverse Method, Backlund Transformation and an Infinite Number of Conservation Laws
• Eigen Value Problem with Nonvanishing Potentials
• Inverse Scattering Method for the Nonlinear Evolution Equations under Nonvanishing Conditions
• Matter-Wave Solitons in an F=1 Spinor Bose–Einstein Condensate
• N-Soliton Collision in the Manakov Model
• DYNAMICS OF BRIGHT MATTER WAVE SOLITONS IN A BOSE–EINSTEIN CONDENSATE

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