Breadcrumb

Explicit asymptotics for waves and vortices on the shallow water created by spatially localized sources with small amplitudes

Fri 22 February 2013, 14:00

Sergey Dobrokhotov
A.Ishlinski Institute for problem in mechanics of Russian academy of sciences and Moscow institute

Mathematical Physics

Organiser: Nina Snaith

ABSTRACT
First we discuss the asymptotic solutions of the Cauchy problem with the spatially localized initial data and right hand side for the linear Shallow water equation over nonuniform bottom. We show that the special choice of sources gives possibility to express the asymptotic solution via elementary or special functions including the situation when the focal (turning) points and cascade of these points can appear on the front. We also show that the vortical part of solution could be viewed as moving focal point. Then we discuss the small dispersion effects and finally a behavior of solutions near the shore (“run-up-problem†in linear 1-D and 2-D cases and nonlinear 1-D case) using the idea that the shore line is the special type of caustics. We apply our consideration to tsunami wave problems.

This work was done together with D.Lozhnikov, V.Nazaikinskii, S.Sekerzh-Zenkovich, A.Shafarevich, B.Volkov and B.Tirozzi