Soliton solutions of some nonlinear evolution equations in shallow water theory

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.

Automated summary

This paper proposes an exponential function method (EFM) to solve the generalized Calogero-Bogoyavlenskii-Schiff equation, (3+1) dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation, and Variant Boussinesq equation. The solitary, cuspon, and periodic wave solutions are obtained and presented graphically. The soliton solutions of these equations play a typical role in expressing various wave transmissions in natural instances, particularly in shallow wave kinetics. The results suggest that EFM is an effective and useful technique for handling nonlinear engineering problems in oceans.