Inverse scattering method for square matrix nonlinear Schrödinger equation under nonvanishing boundary conditions
arXiv:nlin/0603010 · doi:10.1063/1.2423222
Abstract
Matrix generalization of the inverse scattering method is developed to solve the multicomponent nonlinear Schrödinger equation with nonvanishing boundary conditions. It is shown that the initial value problem can be solved exactly. The multi-soliton solution is obtained from the Gel'fand--Levitan--Marchenko equation.
25 pages, 2 figures; (v2) title changed, typos in equations corrected, sec.3.1 modified and extended
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- Controlled Generation of Dark-Bright Soliton Complexes in Two-Component and Spinor Bose-Einstein Condensates
- Painlev{é} singularity structure analysis of three component Gross-Pitaevskii type equations
- Matter-Wave Bright Solitons with a Finite Background in Spinor Bose-Einstein Condensates
- Bogoliubov-de Gennes Soliton Dynamics in Unconventional Fermi Superfluids
- Exhaustive derivation of static self-consistent multi-soliton solutions in the matrix Bogoliubov-de Gennes systems
- Riemann-Hilbert problem for the modified Landau-Lifshitz equation with nonzero boundary conditions
- Tsunami Solitons Emerging from Superconducting Gap
- One-Dimensional Integrable Spinor BECs Mapped to Matrix Nonlinear Schrödinger Equation and Solution of Bogoliubov Equation in These Systems
- Fundamental Analytic Solutions for the Kulish-Sklyanin Model with Constant Boundary Conditions