On a coupled system of shallow water equations admitting travelling wave solutions (Q1664955)

Summary: We consider three inviscid, incompressible, irrotational fluids that are contained between the rigid walls \(y = - h_1\) and \(y = h + H\) and that are separated by two free interfaces \(\eta_1\) and \(\eta_2\). 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.