Some analytical soliton solutions of the nonlinear evolution equations
S. M. Rayhanul Islam, Hanfeng Wang
Abstract
In our manuscript, the (2+1)-dimensional Zakharov-Kuznetsov modified equal width (ZK-MEW) and couple breaking soliton (BS) equations are considered and implemented for the first time using a modified version of the new Kudryashov (MVNK) method. Based on the suggested way, we will extract analytical soliton solutions of the stated equations. The resulting solutions are expressed by sinh, cosh, tanh, coth, csch, sech and their combinations include wave number, phase component, nonlinear coefficient, dispersion coefficient and other free parameters. The obtained solutions are explained in some plots in three-dimensional (3D) and two-dimensional (2D) combined graphs in this paper, which also discusses the effect of the wave phenomena in 2D diagrams. We have compared our solutions and Wazwaz [19] solutions in the present manuscript. However, the wave events come to the ocean engineering and science, the established models are the ones to use because they rule out nonlinearities and dispersion factors present in shallow-water waves and other waves. Finally, the solutions produced help analyze wave interactions in various new structures and high-dimensional models, and they are also helpful for different applications.