On a Coupled System of Shallow Water Equations Admitting Travelling Wave Solutions

Abstract EN

We consider three inviscid, incompressible, irrotational fluids that are contained between the rigid walls y=−h1 and y=h+H and that are separated by two free interfaces η1 and η2.

A generalized nonlocal spectral (NSP) formulation is developed, from which asymptotic reductions of stratified fluids are obtained, including coupled nonlinear generalized Boussinesq equations and (1+1)-dimensional shallow water equations.

A numerical investigation of the (1+1)-dimensional case shows the existence of solitary wave solutions which have been investigated for different values of the characteristic parameters.