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Asymptotic stability of solitary waves for the BenjaminBonaMahony equation
1.  Laboratoire de Mathématiques, Université ParisSud, 91405 Orsay, France 
$(1\partial^2_x)u_t+(u+u^2)_x=0.$
We prove that a solution initially close to a solitary wave, once conveniently translated, converges weakly in $H^1(\mathbb R)$, as time goes to infinity, to a possibly different solitary wave. The proof is based on a Liouville type theorem for the flow close to the solitary waves, and makes an extensive use of a monotonicity property.
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