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Fronts, domain walls and pulses in a generalized Ginzburg-Landau equation*

Published online by Cambridge University Press:  20 January 2009

Jinqiao Duan  and
Philip Holmes
Jinqiao Duan
Affiliation:
Applied Mechanics 104–44California Institute of TechnologyPasadena, California 91125, U.S.A.
Philip Holmes
Affiliation:
Department of Mechanical and Aerospace Engineering and Program in Applied and Computational MathematicsPrinceton UniversityPrinceton, New Jersey 08544, U.S.A.
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Abstract

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We discuss the existence and non-existence of front, domain wall and pulse type traveling wave solutions of a Ginzburg-Landau equation with cubic terms containing spatial derivatives and a fifth order term, in both subcritical and supercritical cases. Our results appear to be the first rigorous existence and non-existence proofs for the full equation with all possible terms derived from second order perturbation theory present.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 38 , Issue 1 , February 1995 , pp. 77 - 97
Copyright
Copyright © Edinburgh Mathematical Society 1995

References

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