Abstract
In this paper, our work is based on a coupled nonlinear Schr ̈odinger system in a two-mode nonlinear fiber. A (N,m)-generalized Darboux transformation is constructed to derive the Nth-order solutions, where the positive integers N and m denote the numbers of iterative times and of distinct spectral parameters, respectively. Based on the Nth-order solutions and the given steps to perform the asymptotic analysis, it is found that a degenerate dark-bright soliton is the nonlinear superposition of several asymptotic dark-bright solitons possessing the same profile. For those asymptotic dark-bright solitons, their velocities are z-dependent except that one of those velocities could become z-independent under the certain condition, where z denotes the evolution dimension. Those asymptotic dark-bright solitons are reflected during the interaction. When a degenerate dark-bright soliton interacts with a nondegenerate/degenerate dark-bright soliton, the interaction is elastic, and the asymptotic bound-state dark-bright soliton with z-dependent or z-independent velocity could take place under certain conditions. Our study extends the investigation on the degenerate solitons from the bright soliton case for the scalar equations to the dark-bright soliton case for a coupled system.
Construction of traveling wave solutions of the (2+1)-dimensional Heisenberg ferromagnetic spin chain equation
