# American Institute of Mathematical Sciences

October  2005, 12(5): 973-982. doi: 10.3934/dcds.2005.12.973

## Smoothing effect of the generalized BBM equation for localized solutions moving to the right

 1 Laboratoire de Mathématiques, Université Paris-Sud, 91405 Orsay, France

Received  November 2003 Revised  August 2004 Published  February 2005

We prove $C^\infty$ smoothness and uniform exponential decay for $H^1$-localized solutions moving to the right of the generalized BBM equation. For that purpose we use a monotonicity property for solution which are not necessarily close to solitary waves.
Citation: Khaled El Dika. Smoothing effect of the generalized BBM equation for localized solutions moving to the right. Discrete and Continuous Dynamical Systems, 2005, 12 (5) : 973-982. doi: 10.3934/dcds.2005.12.973
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