The $N$-soliton formulas for a multi-component modified nonlinear Schrödinger system with nonzero boundary conditions (Workshop on Nonlinear Water Waves)

Abstract

The present paper provides the dark N-soliton solution for a multi-component modified nonlinear Schrödinger (NLS) system with plane-wave boundary conditions, as well as the bright-dark Nsoliton solution with mixed zero and plane-wave boundary conditions. The N-soliton formulas obtained here include as special cases the existing soliton solutions of the NLS and derivative NLS equations and their integrable multi-component analogs. The new features of soliton solutions are discussed. In particular, it is shown that the N constraints must be imposed on the amplitude parameters of solitons in constructing the dark N-soliton solution with plane-wave boundary conditions. For mixed type boundary conditions, the structure of soliton solutions is found to be more explicit than that of dark soliton solutions since no constraints are imposed on the soliton parameters. Last, we comment on an integrable multi-component system associated with the first negative flow of the multi-component derivative NLS hierarchy.