On Soliton Solutions of Perturbed Boussinesq and KdV-Caudery-Dodd-Gibbon Equations

Muhammad Imran Asjad,Muhammad Bilal Riaz,Hamood Ur Rehman,Ali Akgül,Jan Awrejcewicz,Zunaira Ishfaq

doi:10.3390/coatings11111429

Muhammad Imran Asjad, Muhammad Bilal Riaz + Show 4 more

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https://doi.org/10.3390/coatings11111429

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Abstract

Nonlinear science is a fundamental science frontier that includes research in the common properties of nonlinear phenomena. This article is devoted for the study of new extended hyperbolic function method (EHFM) to attain the exact soliton solutions of the perturbed Boussinesq equation (PBE) and KdV–Caudery–Dodd–Gibbon (KdV-CDG) equation. We can claim that these solutions are new and are not previously presented in the literature. In addition, 2d and 3d graphics are drawn to exhibit the physical behavior of obtained new exact solutions.

Highlights

The analysis of exact solutions to nonlinear evolution equations (NLEEs) is fundimental to the study of nonlinear properties
Efficient techniques for extracting exact solutions to NLEEs have been reported by many researchers, such as the Jacobi elliptic function expansion method [9,10,11], tanh method [12,13,14], exp-function method [15,16], F-expansion methods [17,18,19,20,21], ansatz function method [22], auxiliary differential equation method [23,24], homogeneous balance method [25,26], (G /G)-expansion method [27,28], modified simple equation method [29], trail function method [30,31], the variational method [32,33,34], subODE method [35], function transformation method [36,37,38], new extended hyperbolic function method (EHFM) [39,40,41,42], and many more
A modern technique, namely new EHFM [39,40,41], is utilized to retrieve solutions to perturbed Boussinesq equation (PBE) and KdV-CDG equations arising in acoustic waves, long water waves, quantum mechanics, plasma waves, and nonlinear optics

Summary

Introduction

The analysis of exact solutions to nonlinear evolution equations (NLEEs) is fundimental to the study of nonlinear properties. Efficient techniques for extracting exact solutions to NLEEs have been reported by many researchers, such as the Jacobi elliptic function expansion method [9,10,11], tanh method [12,13,14], exp-function method [15,16], F-expansion methods [17,18,19,20,21], ansatz function method [22], auxiliary differential equation method [23,24], homogeneous balance method [25,26], (G /G)-expansion method [27,28], modified simple equation method [29], trail function method [30,31], the variational method [32,33,34], subODE method [35], function transformation method [36,37,38], new EHFM [39,40,41,42], and many more. The main advantage of using method EHFM is to construct the dark, bright, singular, and periodic soliton solutions

The Extended Hyperbolic Function Method Consider nonlinear PDEs as follows

Conclusions