The stability of bright–dark solitons in defocusing coupled nonlinear Schrödinger equation

Abstract

The Darboux transformation is a classical method to generate the solitonic solutions for the integrable equations. In this work, we develop the Darboux transformation to analyze the spectral stability of bright–dark soliton for defocusing coupled nonlinear Schrödinger equation (CNLSE) by combining the squared-eigenfunction method, which can be readily extended to the other 1+1dimensional integrable system. It is shown that the bright–dark soliton solutions for the defocusing CNLSE are spectral stable.

Keywords

• Defocusing coupled nonlinear Schrödinger equation
• Stability
• Bright–dark soliton
• Squared eigen-function method
• Darboux transformation