Topological solitons, cnoidal waves and conservation laws of coupled wave equations

Abstract

In this paper a few coupled wave equations that arise in the dynamics of two-layered shallow water waves in ocean shores and beaches have been studied. The mapping method is applied to extract cnoidal waves and solitary wave solutions to the coupled Korteweg–de Vries (KdV) equation, coupled Boussinesq equation and the coupled Whitham–Broer–Kaup equation. The ansatz method is also applied to obtain topological 1-solution to the coupled KdV equation with power law nonlinearity. The multiplier method then gives a few conserved quantities of the coupled KdV equation.