# American Institute of Mathematical Sciences

November  2009, 12(4): 671-692. doi: 10.3934/dcdsb.2009.12.671

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

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

Received  May 2008 Revised  May 2009 Published  August 2009

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.
Citation: Borys Alvarez-Samaniego, Pascal Azerad. Existence of travelling-wave solutions and local well-posedness of the Fowler equation. Discrete and Continuous Dynamical Systems - B, 2009, 12 (4) : 671-692. doi: 10.3934/dcdsb.2009.12.671
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