Study of explicit travelling wave solutions of nonlinear evolution equations

Abstract

The Bernoulli Sub-ODE approach is used in this study to look for comprehensive travelling wave solutions to the nonlinear evolution equations (NLEEs). The analysis in the present paper shows the existence of travelling waves for the time-regularized long-wave (TRLW) equation, the modified Korteweg–de Vries –Zakharov–Kuznetsov (mKdV–ZK) equation, and the (2+1)-dimensional Zoomeron equation. The outcomes demonstrate the richness of explicit solutions of the studied models. As a result, precise solitary wave solutions to the studied problems, such as kink waves, singular kink waves, dark soliton, and periodic waves are found. The phase plane is briefly examined after the determination of the Hamiltonian function. Using Maple 13, we validated the accuracy of the obtained solutions by reintroducing them into the original equation. We will demonstrate how the amplitudes and wave profiles are impacted by free parameters. In this article, we firmly establish that the wave amplitude varies as the free parameters change. It is demonstrated that the technique is efficient and applicable to several different NLEEs in mathematical physics.