A Generalized KdV Equation of Neglecting the Highest-Order Infinitesimal Term and Its Exact Traveling Wave Solutions

Abstract

We study a generalized KdV equation of neglecting the highest order infinitesimal term, which is an important water wave model. Some exact traveling wave solutions such as singular solitary wave solutions, semiloop soliton solutions, dark soliton solutions, dark peakon solutions, dark loop-soliton solutions, broken loop-soliton solutions, broken wave solutions of U-form and C-form, periodic wave solutions of singular type, and broken wave solution of semiparabola form are obtained. By using mathematical software Maple, we show their profiles and discuss their dynamic properties. Investigating these properties, we find that the waveforms of some traveling wave solutions vary with changes of certain parameters.