New solitary wave in shallow water, plasma and ion acoustic plasma via the GZK-BBM equation and the RLW equation

Abstract

This work obtains the disguise version of exact solitary wave solutions of the generalized (2+1)-dimensional Zakharov-Kuznetsov–Benjamin-Bona-Mahony and the regularized long wave equation with some free parameters via modified simple equation method (MSE). Usually the method does not give any solution if the balance number is more than one, but we apply MSE method successfully in different way to carry out the solutions of nonlinear evolution equation with balance number two. Finally some graphical results of the velocity profiles are presented for different values of the material constants. It is shown that this method, without help of any symbolic computation, provide a straightforward and powerful mathematical tool for solving nonlinear evolution equation.

Keywords

• The modified simple equation method
• Exact traveling wave solution
• Generalized Zakharov-Kuznetsov–Benjamin-Bona-Mahony (GZK-BBM)
• The regularized long wave equation
• Balance number
• Nonlinear evolution equations (NLEEs)