Coexistence of nontrivial solutions of the one-dimensional Ginzburg-Landau equation : a computer-assisted proof

Authors: Correc, Anaïs; Lessard, Jean-Philippe
Abstract: In this paper, Chebyshev series and rigorous numerics are combined to compute solutions of the Euler-Lagrange equations for the one-dimensional Ginzburg-Landau model of superconductivity. The idea is to recast solutions as fixed points of a Newton-like operator defined on a Banach space of rapidly decaying Chebyshev coefficients. Analytic estimates, the radii polynomials and the contraction mapping theorem are combined to show existence of solutions near numerical approximations. Coexistence of as many as seven nontrivial solutions is proved.
Document Type: Article de recherche
Issue Date: 8 October 2014
Open Access Date: 16 May 2016
Document version: AM
This document was published in: European journal of applied mathematics, Vol. 26 (1), 33–60 (2015)
Cambridge University Press
Alternative version: 10.1017/S0956792514000308
Collection:Articles publiés dans des revues avec comité de lecture

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