New Exact Superposition Solutions to KdV2 Equation

Abstract

New exact solutions to the KdV2 equation (also known 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 A/2dn2[B(x-vt),m]±m cn[B(x-vt),m]dn[B(x-vt),m]+D in the form of periodic functions found in the paper complement other forms of exact solutions to KdV2 obtained earlier, that is, the solitonic ones and periodic ones given by single cn2 or dn2 Jacobi elliptic functions.