Soliton solutions of some nonlinear evolution equations in shallow water theory

Abstract

This paper proposes some soliton solutions of a generalized Calogero–Bogoyavlenskii–Schiff equation, a (3+1) dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov and a Variant Boussinesq equations. We presented a exponential function method (EFM) for solving the considered evolution equations. The solitary, cuspon and periodic wave solutions are acquired and presented graphically. The soliton solutions of considered equations play a typical role for expressing kinds of wave transmission in any natural instance, particularly in shallow wave kinetics. The results suggest that EFM is effective and useful technique to handle non-linear engineering problems in oceans.

Keywords

• Exp-function method
• Shallow-water waves
• Generalized Calogero–Bogoyavlenskii–Schiff equation
• (3+1) dimensional Modified-kdv–Zakharov–Kuznetsov equation
• The Variant Boussinesq equation