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

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

References in corpus (2)

• Dark solitons in F=1 spinor Bose--Einstein condensate
• N-soliton collision in the Manakov model

Cited by in corpus (4)

• Perturbation theory for bright spinor Bose--Einstein condensate solitons
• Multicomponent Bright Solitons in F = 2 Spinor Bose-Einstein Condensates
• Full-time dynamics of modulational instability in spinor Bose-Einstein condensates
• Matter-Wave Bright Solitons with a Finite Background in Spinor Bose-Einstein Condensates