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Bounded solutions for an ordinary differential system from the Ginzburg–Landau theory

Published online by Cambridge University Press:  14 August 2020

Anne Beaulieu*
Affiliation:
LAMA, Univ. Paris Est Creteil, Univ. Gustave Eiffel, UPEM, CNRS, F-94010, Créteil, France ([email protected])

Abstract

In this paper, we look at a linear system of ordinary differential equations as derived from the two-dimensional Ginzburg–Landau equation. In two cases, it is known that this system admits bounded solutions coming from the invariance of the Ginzburg–Landau equation by translations and rotations. The specific contribution of our work is to prove that in the other cases, the system does not admit any bounded solutions. We show that this bounded solution problem is related to an eigenvalue problem.

Type
Research Article
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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