Existence of travelling-wave solutions and local well-posedness of the Fowler equation

Borys Alvarez-Samaniego; Pascal Azerad

doi:10.3934/dcdsb.2009.12.671

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2009, Volume 12, Issue 4: 671-692. Doi: 10.3934/dcdsb.2009.12.671

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Existence of travelling-wave solutions and local well-posedness of the Fowler equation

Borys Alvarez-Samaniego^1, and
Pascal Azerad^1,

1.
Institut de Mathématiques et Modélisation de Montpellier (I3M)-UMR 5149 CNRS, Université Montpellier 2, CC 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5

Received: May 2008

Revised: May 2009

Published: November 2009

Abstract / Introduction Related Papers Cited by

Abstract

We study the existence of travelling-waves and local well-posedness in a subspace of $C_b^1(\R)$ for a nonlinear evolution equation recently proposed by Andrew C. Fowler to describe the dynamics of dunes. The travelling-waves we obtained however, were more bore-like than solitary-wave-like.

Keywords:

Nonlocal evolution equation,
travelling-wave.

Mathematics Subject Classification: Primary: 47J35, 35G25; Secondary: 76B25.

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