===  Maria Eugenia MARTINEZ   === 
== The soliton problem for the Zakharov water waves problem with slowly varying bottom.  ==


Zakharov water waves arises as a free surface model for an irrotational and incompressible fluid under the influence of gravity. Such fluid is
considered in a domain with rigid bottom (described as ha(x)) and a free surface. When considering the pressure over the surface, Amick-Kirchgässner proved the existence of solitary waves Qc (solutions that maintain its shape as they travel in time) of speed c for the flat-bottom case (a=1). In this talk, we are interested  in the analysis of the behavior of the solitary wave solution of the flat-bottom problem when the bottom actually presents a (slight) change at some point. We construct a solution to the Zakharov water waves system with non-flat bottom that is time assympotic (as time t tends to - infinity) to the Amick-Kirchgässner soliton Q_c