Peaked solitary waves and shock waves of the Degasperis-Procesi-Kadomtsev-Petviashvili equation

Abstract

In this study, we establish the existence and nonexistence of smooth and peaked solitary wave solutions (or periodic) to the Degasperis-Procesi-Kadomtsev-Petviashvili (DP-KP) equation with a weak transverse effect. We have also shown that DP-KP equation possesses periodic shock waves similar to that of the Degasperis-Procesi equation.

Keywords

• solitary waves
• shock waves
• degasperis-procesi-kadomtsev-petviashvili equation
• degasperis-procesi equation
• 35q53
• 35g25
• 76b15
• 76b25