Solitary Wave Solution of Nonlinear PDEs Arising in Mathematical Physics

Abstract The solution of nonlinear mathematical models has much importance and in soliton theory its worth has increased. In the present article, we have investigated the Caudrey-Dodd-Gibbon and Pochhammer-Chree equations, to discuss the physics of these equations and to attain soliton solutions. The exp(−ϕ(ζ ))-expansion technique is used to construct solitary wave solutions. A wave transformation is applied to convert the problem into the form of an ordinary differential equation. The drawn-out novel type outcomes play an essential role in the transportation of energy. It is noted that in the study, the approach is extremely reliable and it may be extended to further mathematical models signified mostly in nonlinear differential equations.

Download Full-text

Solitary wave solution of nonlinear Bogoyavlenskii system by variational analysis method

International Journal of Modern Physics B ◽

10.1142/s0217979222500151 ◽

2021 ◽

Author(s):

KangLe Wang

Keyword(s):

Solitary Wave ◽

Variational Analysis ◽

Solitary Wave Solution ◽

Solitary Wave Solutions ◽

Analysis Method ◽

Soliton Theory ◽

Practical Applications ◽

The Road ◽

Wave Solutions ◽

First Time

In this work, the Bogoyavlenskii system (BS) and fractal BS are investigated by variational method for the first time. An efficient and simple scheme is proposed to seek their exact solitary wave solutions, which is called variational analysis method. The novel scheme requires only two steps, making it much attractive in practical applications, and a good result is obtained. This paper cleans up the road to the exact solitions, and it sheds a new light on the soliton theory. Finally, the physical properties of solitary wave solutions obtained are analyzed by some simulation figures.

Download Full-text

The Solitary Wave Solution for Quantum Plasma Nonlinear Dynamic Model

Advances in Mathematical Physics ◽

10.1155/2020/5602373 ◽

2020 ◽

Vol 2020 ◽

pp. 1-6

Author(s):

Yihu Feng ◽

Lei Hou

Keyword(s):

Solitary Wave ◽

Dynamic Model ◽

Nonlinear Dynamic ◽

Wave Solution ◽

Solitary Wave Solution ◽

Wave Transformation ◽

Quantum Plasma ◽

Nonlinear Dynamic Model ◽

Plasma System ◽

System A

In this paper, we discussed the quantum plasma system. A nonlinear dynamic disturbed model is studied. We used the undetermined coefficients method, dimensionless transformation and traveling wave transformation for the hyperbolic functions, and perturbation theory and method; then, the solitary wave solution for the quantum plasma nonlinear dynamic model is solved. Finally, the characteristics of the corresponding physical quantity are described.

Download Full-text

On the Exact Soliton Solutions of Some Nonlinear PDE by Tan-Cot Method

GUB Journal of Science and Engineering ◽

10.3329/gubjse.v5i1.47898 ◽

2018 ◽

Vol 5 (1) ◽

pp. 31-36

Author(s):

Md Monirul Islam ◽

Muztuba Ahbab ◽

Md Robiul Islam ◽

Md Humayun Kabir

Keyword(s):

Solitary Wave ◽

Acoustic Waves ◽

Water Waves ◽

Wave Equations ◽

Rectangular Channel ◽

Soliton Solutions ◽

Boussinesq Equations ◽

Travelling Wave ◽

Ion Acoustic Waves ◽

Analytical System

For many solitary wave applications, various approximate models have been proposed. Certainly, the most famous solitary wave equations are the K-dV, BBM and Boussinesq equations. The K-dV equation was originally derived to describe shallow water waves in a rectangular channel. Surprisingly, the equation also models ion-acoustic waves and magneto-hydrodynamic waves in plasmas, waves in elastic rods, equatorial planetary waves, acoustic waves on a crystal lattice, and more. If we describe all of the above situation, we must be needed a solution function of their governing equations. The Tan-cot method is applied to obtain exact travelling wave solutions to the generalized Korteweg-de Vries (gK-dV) equation and generalized Benjamin-Bona- Mahony (BBM) equation which are important equations to evaluate wide variety of physical applications. In this paper we described the soliton behavior of gK-dV and BBM equations by analytical system especially using Tan-cot method and shown in graphically. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 5(1), Dec 2018 P 31-36

Download Full-text

The novel multi-solitary wave solution to the fifth-order KdV equation

Chinese Physics ◽

10.1088/1009-1963/13/10/004 ◽

2004 ◽

Vol 13 (10) ◽

pp. 1606-1610 ◽

Cited By ~ 3

Author(s):

Zhang Yi ◽

Chen Deng-Yuan

Keyword(s):

Solitary Wave ◽

Wave Solution ◽

Solitary Wave Solution ◽

Kdv Equation ◽

The Novel ◽

Fifth Order

Download Full-text

Abundant Explicit and Exact Solutions for the Variable Coefficient mKdV Equations

Abstract and Applied Analysis ◽

10.1155/2013/109690 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Xiaoxiao Zheng ◽

Yadong Shang ◽

Yong Huang

Keyword(s):

Solitary Wave ◽

Elliptic Function ◽

Constant Coefficient ◽

Wave Solution ◽

Integral Method ◽

Solitary Wave Solution ◽

First Integral ◽

Mkdv Equation ◽

Variable Coefficients ◽

First Integral Method

This paper is concerned with the variable coefficients mKdV (VC-mKdV) equation. First, through some transformation we convert VC-mKdV equation into the constant coefficient mKdV equation. Then, using the first integral method we obtain the exact solutions of VC-mKdV equation, such as rational function solutions, periodic wave solutions of triangle function, bell-shape solitary wave solution, kink-shape solitary wave solution, Jacobi elliptic function solutions, and Weierstrass elliptic function solution. Furthermore, with the aid of Mathematica, the extended hyperbolic functions method is used to establish abundant exact explicit solution of VC-mKdV equation. By the results of the equation, the first integral method and the extended hyperbolic function method are extended from the constant coefficient nonlinear evolution equations to the variable coefficients nonlinear partial differential equation.

Download Full-text