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

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