New closed-form soliton solutions for the tzitzeica dodd bullough equation arising nonlinear optics via three distinct re-liable approaches

Faisal Hawlader,Nahida Akter

doi:10.14419/ijpr.v9i1.31271

Abstract

Tzitzeica Dodd Bullough (TDB) equation appears in the field of quantum field theory and nonlinear optics. In this article, we extracted abundant new soliton solutions with free choice of arbitrary parameters to the Tzitzeica-Dodd-Bullough (TDB) equation through the three separate methods such as the enhanced -expansion method, the improved -expansion method and the -expansion method by means of the wave transformation and the Painleve property. In these schemes, we formally derived some new closed form soliton solutions of the TDB equation through with symbolic computation package Maple. Soliton solutions are expressed by hyperbolic function, trigonometric function and rational function. The attained solutions are verified by symbolic computation software Maple 17. The attained solutions can be demonstrated by two-dimensional (2D) and three-dimensional (3D) graphs. Finally, it can be concluded that the adopted methods are very effective and well-suited to find new closed-form soliton solutions to the other nonlinear evaluation equations (NLEEs) with integer or fractional order.Â

Highlights

Nonlinear evolution equations survive naturally everywhere in the world in various fields of applied mathematics, mathematical physics and engineering, especially plasma physics, solid state physics, plasma waves, chemical kinematics, optical fibers, fluid dynamics and etc
Nonlinear evolution equations (NLEEs) have a great importance to mark out complex physical phenomena in the real-world problems
It is well recognized that to looking for exact analytical solution of NLEEs arising in mathematical physics plays an imperative role in the study of nonlinear physical phenomena and optics

Summary

Introduction

Nonlinear evolution equations survive naturally everywhere in the world in various fields of applied mathematics, mathematical physics and engineering, especially plasma physics, solid state physics, plasma waves, chemical kinematics, optical fibers, fluid dynamics and etc. Researchers have made a perform to ongoing research works and produce the new exact solitary wave solutions from nonlinear evolution equations. They developed numerous potential and useful techniques, such as, the homogeneous balance method [4], Hirota’s bilinear method [5], the trial function method [6], the tanh-function method [7], the theta function method [8,9], the extended tanh-function method [10], the modified extended tanh-function method [11], the hyperbolic function method [12], the sine–cosine method [13], the inverse scattering transform [14], the Jacobi elliptic function expansion [15], the Homotopy perturbation methods [16], the auxiliary equation method [17], the first integral method [18], the modified Kudryashov method [19], the generalized Kudryashov method [20], the (G '/ G) -expansion method [21], the improved (G '/ G) -expansion method [22] and so on.

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Results

Conclusion