On the exponential solutions to three extracts from extended fifth-order KdV equation

Abstract

An extended fifth order Korteweg-de-Vries (efKdV) equation is an important equation in fluids dynamics for the description of nonlinear wave processes, and contains quite a number of KdV-type equations including the Sawada-Kotera equation, the Caudrey-Dodd-Gibbon equation, the Lax equation, the Kaup-Kuperschmidt equation and the Ito equation among others. However, in this paper, we examine the efKdV by extracting three different fifth order Korteweg-de-Vries (fKdV) equations. Solitary wave solutions to the extracts are found by means of an exponential function ansatz specifically constructed for the study. The obtained solutions can be used in description of shallow-water waves.