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

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. It is shown that the investigated equations set has local minima, global minima, local maximum, and the points refer to saddle points. 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.The profiles of dimensionless energy density of the equations set for the different initial values of are given. The dependence of the parameters of the system m₁, m₂ and the total energy M on the initial values of c₀ is investigated.