New exact superposition solutions to KdV2 equation

Abstract

New exact solutions to the KdV2 equation (known also as the extended KdV equation) are constructed. The KdV2 equation is a second order approximation of the set of Boussinesq's equations for shallow water waves which in first order approximation yields KdV. The exact solutions ~$\frac{A}{2}\left(\dn^2[B(x-vt),m]\pm \sqrt{m}\,\cn [B(x-vt),m]\dn [B(x-vt),m]\right)+D$~ in the form of periodic functions found in the paper complement other forms of exact solutions to KdV2 obtained earlier, i.e., the solitonic ones and periodic ones given by a single $\cn^2$ or $\dn^2$ Jacobi elliptic functions.