Qualitative analysis of the eigenvalue problem for two coupled Ginzburg-Landau equations

TL;DR

This paper numerically investigates the eigenvalue problem for two coupled Ginzburg-Landau equations, analyzing fixed points, phase portraits, and parameter dependencies to understand the system's behavior.

Contribution

It provides a detailed numerical analysis of the eigenvalue problem for coupled Ginzburg-Landau equations, including fixed point classification and phase space analysis.

Findings

Identification and classification of fixed points.

Phase portraits illustrating system dynamics.

Dependence of total energy on initial conditions.

Abstract

Eigenvalue problem for two coupled Ginzburg-Landau equations is numerically investigated. The fixed points of corresponding equations system are found. The classification of these points is made. The phase portraits of corresponding ordinary differential equations and the dependence of some parameters of the equations system and the total energy on the initial values are given.