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November  2008, 7(6): 1345-1359. doi: 10.3934/cpaa.2008.7.1345

Numerical mountain pass solutions of Ginzburg-Landau type equations

Dmitry Glotov 1, and  P. J. McKenna 1,

1. 

Department of Mathematics, 196 Auditorium Road, Unit 3009, University of Connecticut, Storrs, CT 06269-3009, United States, United States

Received  August 2007 Revised  May 2008 Published  August 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.
Keywords: mountain pass method, Ginzburg-Landau equations, numerical solution..
Mathematics Subject Classification: Primary: 35J60, 35J50; Secondary: 65N9.
Citation: Dmitry Glotov, P. J. McKenna. Numerical mountain pass solutions of Ginzburg-Landau type equations. Communications on Pure & Applied Analysis, 2008, 7 (6) : 1345-1359. doi: 10.3934/cpaa.2008.7.1345
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