On the exact solutions to some system of complex nonlinear models

Tukur Abdulkadir Sulaiman,Haci Mehmet Baskonus,Hasan Bulut

doi:10.2478/amns.2020.2.00007

Abstract

Abstract In this manuscript, the application of the extended sinh-Gordon equation expansion method to the Davey-Stewartson equation and the (2+1)-dimensional nonlinear complex coupled Maccari system is presented. The Davey-Stewartson equation arises as a result of multiple-scale analysis of modulated nonlinear surface gravity waves propagating over a horizontal seabed and the (2+1)-dimensional nonlinear complex coupled Maccari equation describes the motion of the isolated waves, localized in a small part of space, in many fields such as hydrodynamic, plasma physics, nonlinear optics. We successfully construct some soliton, singular soliton and singular periodic wave solutions to these two nonlinear complex models. The 2D, 3D and contour graphs to some of the obtained solutions are presented.

Highlights

For the past two decades, the investigations of various travelling wave solutions to the nonlinear evolution equations have attracted the attentions of many scientist from all over the world
In this study, we present the application of the extended sinh-Gordon equation expansion method (ShGEEM) [52] to the Davey-Stewartson equation [53] and the (2+1)-dimensional nonlinear complex coupled Maccari system [54, 55]
The reported results in this study have some physical meanings, for instance; the hyperbolic tangent arises in the calculation of magnetic moment and rapidity of special relativity, the hyperbolic secant arises in the profile of a laminar jet, and hyperbolic cotangent arises in the Langevin function for magnetic polarization [72]

Summary

Introduction

For the past two decades, the investigations of various travelling wave solutions to the nonlinear evolution equations have attracted the attentions of many scientist from all over the world. Nonlinear evolution equations (NLEEs) are used in describing many complex phenomena the arise on daily basis in the various fields of nonlinear sciences, such as; plasmas physics, quantum mechanics, biosciences, chemistry, water waves and so on. In this study, we present the application of the extended sinh-Gordon equation expansion method (ShGEEM) [52] to the Davey-Stewartson equation [53] and the (2+1)-dimensional nonlinear complex coupled Maccari system [54, 55]. Several attempts by different scientists have been made to investigate Eq (1.2) [64,65,66,67,68,69,70,71]

The Extended ShGEEM

Application

Conclusion