Bifurcations and spectral stability of solitary waves in coupled nonlinear Schrodinger equations

We study bifurcations and spectral stability of solitary waves in coupled nonlinear Schrodinger (CNLS) equations on the line. We assume that the coupled equations possess a solution of which one component is identically zero, and call it a fundamental solitary wave. We establish criteria under which the fundamental solitary wave undergoes a pitchfork bifurcation, and utilize the Hamiltonian-Krein index theory and Evans function technique to determine the spectral and/or orbital stability of the bifurcated solitary waves as well as that of the fundamental one under some nondegenerate conditions which are easy to verify, compared with those of the previous results. We apply our theory to a cubic nonlinearity case and give numerical evidences for the theoretical results. & COPY; 2023 Elsevier Inc. All rights reserved.

Automated summary

This article studies bifurcations and spectral stability of solitary waves in coupled nonlinear Schrodinger (CNLS) equations on the line. Under the assumption that the coupled equations possess a solution in which one component is identically zero, called a fundamental solitary wave, the authors establish criteria for the pitchfork bifurcation of the fundamental solitary wave. The authors utilize the Hamiltonian-Krein index theory and Evans function technique to determine the spectral and/or orbital stability of the bifurcated solitary waves and the fundamental one under nondegenerate conditions that are easy to verify compared to previous results. The theory is applied to a cubic nonlinearity case, and numerical evidence is provided for the theoretical results.