Traveling wave solutions using the variational method and the tanh method for nonlinear coupled equations

This paper applied both the tanh and the He’s variational iteration methods for analytic study for the nonlinear coupled Kortewge–de Vries (shortly, KdV) equations. Compared with existing sophisticated approaches, the proposed methods gives more general exact traveling wave solutions without much extra effort. Finally, we present an application to shallow water equations using the two methods, the calculations demonstrate the effectiveness and convenience of the He’s variational method for nonlinear coupled equations.