Mathematical analysis of some new adequate broad-ranging soliton solutions of nonlinear models through the recent technique

Abstract

The Bogoyavlenskii and the simplified modified Camassa-Holm (SMCH) models are studied through the recent technique namely auxiliary equation method in this paper. The Bogoyavlenskii model is more significant in shallow water wave, solitary wave and one dimension lattices. And the SMCH model is explained the Riemann waves along two spatial dimensions, periodic solitary and cross-solitary wave, and more. The novelty of this article is to examine the sufficient, adequate broad-ranging, and further general soliton solutions of the models by utilizing the auxiliary equation approach processing complex wave transformation which are not exist in the recent literature. The finding of this study demonstrates that the examined solutions exhibit that the employed technique is compatible, functional, straightforward and more effective. The accuracy of the acquired solutions is confirmed by reintroducing them into the original models and also the wave structures of the solutions are explained by depicting figures by means of the Wolfram Mathematica program.

Keywords

• 35C08
• 35K99
• 35P99
• 26A33
• 34K37