General<i>N</i>-soliton solution to a vector nonlinear Schrödinger equation

Abstract

We consider a general N-soliton solution to a vector nonlinear Schrödinger (NLS) equation of all possible combinations of nonlinearities including all-focusing, all-defocusing and mixed types. Based on the KP hierarchy reduction method, we firstly construct general two-bright-one-dark and one-bright-two-dark soliton solutions in a three-coupled NLS equation, then we extend our analysis to a vector NLS equation to obtain a general N-soliton solution in Gram determinant form. This formula unifies the bright, dark and bright-dark soliton solutions, which have been widely studied in the literature. The conditions for the existence of all types of soliton solutions with all possible combinations of nonlinearities are elucidated.

Identifiers

DOI

10.1088/1751-8113/47/35/355203

Citations and references