Optical soliton solutions to the (2+1)-dimensional Chaffee\u2013Infante equation and the dimensionless form of the Zakharov equation

M Ali Akbar,Jobayer Hussain,Norhashidah Hj Mohd Ali

doi:10.1186/s13662-019-2377-9

Abstract

The (2+1)-dimensional Chaffee–Infante equation and the dimensionless form of the Zakharov equation have widespread scopes of function in science and engineering fields, such as in nonlinear fiber optics, the waves of electromagnetic field, plasma physics, the signal processing through optical fibers, fluid dynamics, coastal engineering and remarkable to model of the ion-acoustic waves in plasma, the sound waves. In this article, the first integral method has been assigned to search closed form solitary wave solutions to the previously proposed nonlinear evolution equations (NLEEs). We have constructed abundant soliton solutions and discussed the physical significance of the obtained solutions of its definite values of the included parameters through depicting figures and interpreted the physical phenomena. It has been shown that the first integral method is powerful, convenient, straightforward and provides further general wave solutions to diverse NLEEs in mathematical physics.

Highlights

Nonlinearity is a fascinating element of nature and many scientists consider nonlinear science as the most important frontier for the fundamental understanding of nature
Motivated by the ongoing research, in this article, we have examined the (2 + 1)dimensional Chaffee–Infante equation and the dimensionless form of the Zakharov equation (ZE) through the first integral method to extract closed form solitary wave solutions and solitons
Since it is very difficult to examine the closed form wave solutions to the generalized Zakharov equation (GZE) due to strong nonlinearity and if we set b1 = –b, b2 = 0, F(|q|2) = |q|2γ and γ = 1, the GZE is converted into the dimensionless form of the Zakharov equation, in this article, we have studied the dimensionless form of the ZE (64) and (65)

Summary

Introduction

Nonlinearity is a fascinating element of nature and many scientists consider nonlinear science as the most important frontier for the fundamental understanding of nature. Motivated by the ongoing research, in this article, we have examined the (2 + 1)dimensional Chaffee–Infante equation and the dimensionless form of the Zakharov equation (ZE) through the first integral method to extract closed form solitary wave solutions and solitons. As ξ0 is an unspecified constant, we might set ξ0 = 1 into (26), we obtain the subsequent wave solution: u(x, y, t) = ±i tan 1√ –2α(x + y – σ t)

Results

Conclusion