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

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

2006-03-03

arxiv.org/abs/nlin/0603010v2

J. Math. Phys. 48, 013507 (2007)

Nonlinear Sciences

Exactly Solvable and Integrable Systems

25 pages, 2 figures; (v2) title changed, typos in equations corrected, sec.3.1 modified and extended

Scientific paper

10.1063/1.2423222

Matrix generalization of the inverse scattering method is developed to solve
the multicomponent nonlinear Schr\"odinger 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.

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