Solitary wave and shock wave solutions of (1+1)-dimensional perturbed Klein-Gordon,(1+1)-dimensional Kaup-Keperschmidt and (2+1)-dimensional ZK-BBM equations

Abstract

In this paper, two different types of envelope solitons: solitary wave and shock wave have been obtained for the (1+1)-dimensional perturbed Klein-Gordon, (1+1)- dimensional Kaup-Keperschmidt and (2+1)-dimentional ZK-BBM equations using the solitary wave ansatz. The parameter regimes, for the existence of the solitons are identified during the derivation of the solution. Since, the nonlinear wave is one of the fundamental object of nature and a growing interest has been given to the propagation of nonlinear wave in dynamical system.

Keywords

• Solitary wave solution
• shock wave solution
• (1+1)-dimensional perturbed Klein-Gordon equation
• (1+1)-dimensional Kaup-Keperschmidt equation
• (2+1)- dimentional ZK-BBM equation
• solitary wave ansatz