Closed-Form Solutions and Conserved Vectors of a Generalized (3+1)-Dimensional Breaking Soliton Equation of Engineering and Nonlinear Science

Chaudry Masood Khalique,Oke Davies Adeyemo

doi:10.3390/math8101692

Abstract

In this article, we examine a (3+1)-dimensional generalized breaking soliton equation which is highly applicable in the fields of engineering and nonlinear sciences. Closed-form solutions in the form of Jacobi elliptic functions of the underlying equation are derived by the method of Lie symmetry reductions together with direct integration. Moreover, the (G′/G)-expansion technique is engaged, which consequently guarantees closed-form solutions of the equation structured in the form of trigonometric and hyperbolic functions. In addition, we secure a power series analytical solution of the underlying equation. Finally, we construct local conserved vectors of the aforementioned equation by employing two approaches: the general multiplier method and Ibragimov’s theorem.

Highlights

It is an indisputable fact that nonlinear evolutionary equations (NLEEs) have provided a great deal of assistance in modeling several real-world problems consisting of diffusion, dispersion and convection that possess nonlinear effects
We find closed-form solutions in the form of elliptic functions by direct integration of the reduced ordinary differential equation
This section is concerned with the construction of closed-form solutions of 3D-gBSe (2) which are obtained by using Lie symmetry analysis, the ( G 0 )3 − ( (G 0) /G )-expansion method and the power series approach

Summary

Introduction

It is an indisputable fact that nonlinear evolutionary equations (NLEEs) have provided a great deal of assistance in modeling several real-world problems consisting of diffusion, dispersion and convection that possess nonlinear effects. Symmetry analysis is one of the most systematic techniques with which to find closed-form solutions of differential equations. It was pioneered, towards the end of the nineteenth century by a Norwegian mathematician, Sophus Lie (1842–1899), who realized that the ad hoc methods for solving differential equations could be unified. This section is concerned with the construction of closed-form solutions of 3D-gBSe (2) which are obtained by using Lie symmetry analysis, the ( G 0 /G )-expansion method and the power series approach. We utilize the general multiplier technique [19] and the Ibragimov’s theorem [44] to derive the conserved vectors

Multiplier Technique

Ibragimov Approach

Conclusions

Methods