Numerical mountain pass solutions of Ginzburg-Landau type equations
Dmitry Glotov, Patrick McKenna · Communications on Pure & Applied Analysis · 2008
We study the numerical solutions of a system of Ginzburg-Landau type equations arising in the thin film model of superconductivity. These solutions are obtained by the Mountain Pass algorithm that was originally developed for semilinear elliptic equations. We prove a key hypothesis of the Mountain Pass theorem and investigate the physical features of the solutions such as the presence, the number, and the location of vortices and the numerical properties such as stability.