Solitary Solutions of the Boiti-Leon-Manna-Pempinelli Equation Using He’S Variational Method

2008 ◽  
Vol 63 (10-11) ◽  
pp. 634-636 ◽  
Author(s):  
Zhao-Ling Tao
Keyword(s):  
Variational Method ◽  
Traveling Wave ◽  
Variational Formulation ◽  
Inverse Method ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Solitary Solutions

A variational formulation is established for the Boiti-Leon-Manna-Pempinelli equation using He’s semi-inverse method; three kinds of traveling wave solutions are obtained.

scholarly journals Fundamental solutions for the long–short-wave interaction system

Open Physics ◽  
2020 ◽  
Vol 18 (1) ◽  
pp. 1093-1099
Author(s):  
Mustafa Inc ◽  
Samia Zaki Hassan ◽  
Mahmoud Abdelrahman ◽  
Reem Abdalaziz Alomair ◽  
Yu-Ming Chu
Keyword(s):  
Fluid Mechanics ◽  
Traveling Wave ◽  
Inverse Method ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Wave Interaction ◽  
Fundamental Solutions ◽  
Short Wave ◽  
Wave Solutions ◽  
Physical Environments

Abstract In this article, the system for the long–short-wave interaction (LS) system is considered. In order to construct some new traveling wave solutions, He’s semi-inverse method is implemented. These solutions may be applicable for some physical environments, such as physics and fluid mechanics. These new solutions show that the proposed method is easy to apply and the proposed technique is a very powerful tool to solve many other nonlinear partial differential equations in applied science.

Data Processing in Abound Solutions of (2 + 1)-dimensional Boussinesq Equation

2014 ◽  
Vol 1056 ◽  
pp. 215-220
Author(s):  
Han Kun Gong ◽  
Xiao Shan Zhao ◽  
Guan Hua Zhao
Keyword(s):  
Data Processing ◽  
Exact Solutions ◽  
Periodic Solutions ◽  
Symbolic Computation ◽  
Traveling Wave ◽  
Function Method ◽  
Boussinesq Equation ◽  
Traveling Wave Solutions ◽  
Wave Solutions ◽  
Solitary Solutions

In this paper, the repeated exp-function method is applied to construct exact traveling wave solutions of the (2+1)-dimensional Boussinesq equation. With aid of symbolic computation, many generalized solitary solutions, periodic solutions and other exact solutions are successfully obtained. Thus, it is proved that the method is straightforward and effective to solve the nonlinear evolutions equations.

EXACT AND APPROXIMATE TRAVELING WAVES OF REACTION-DIFFUSION SYSTEMS VIA A VARIATIONAL APPROACH

2011 ◽  
Vol 09 (02) ◽  
pp. 187-199 ◽  
Author(s):  
MARIANITO R. RODRIGO ◽  
ROBERT M. MIURA
Keyword(s):  
Biological Sciences ◽  
Traveling Wave ◽  
Variational Formulation ◽  
Traveling Wave Solutions ◽  
Reaction Diffusion ◽  
Traveling Wave Solution ◽  
Fourth Degree ◽  
Reaction Diffusion Systems ◽  
Wave Solutions ◽  
Diffusion Systems

Reaction-diffusion systems arise in many different areas of the physical and biological sciences, and traveling wave solutions play special roles in some of these applications. In this paper, we develop a variational formulation of the existence problem for the traveling wave solution. Our main objective is to use this variational formulation to obtain exact and approximate traveling wave solutions with error estimates. As examples, we look at the Fisher equation, the Nagumo equation, and an equation with a fourth-degree nonlinearity. Also, we apply the method to the multi-component Lotka–Volterra competition-diffusion system.

BOUNDED TRAVELING WAVE SOLUTIONS TO THE SHORT PULSE EQUATION

2012 ◽  
Vol 21 (04) ◽  
pp. 1250049
Author(s):  
BINXIAN ZHUANG ◽  
YUANJIANG XIANG ◽  
XIAOYU DAI ◽  
SHUANGCHUN WEN
Keyword(s):  
Traveling Wave ◽  
Short Pulse ◽  
Traveling Wave Solutions ◽  
Short Pulse Equation ◽  
Wave Solutions ◽  
Solitary Solutions

In this paper, we try to find bounded traveling wave solutions to short pulse equation (SPE) under different combinations of the coefficients of SPE. Results show that the global bounded traveling wave solutions to SPE are possible only in the focusing nonlinearity and impossible in the defocusing nonlinearity. The periodic loop or inverted loop, and the periodic hump or inverted hump global bounded traveling solutions are obtained in the focusing nonlinearity for three cases separately. The former can degenerate into loop or inverted loop solitary solutions.

scholarly journals New Exact Solutions of Ion-Acoustic Wave Equations by (G′/G)-Expansion Method

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Wafaa M. Taha ◽  
M. S. M. Noorani ◽  
I. Hashim
Keyword(s):  
Traveling Wave ◽  
Acoustic Waves ◽  
Traveling Wave Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Plasma Physic ◽  
Wave Solutions ◽  
Solitary Solutions ◽  
Petviashvili Equation ◽  
Ion Acoustic

The (G′/G)-expansion method is used to study ion-acoustic waves equations in plasma physic for the first time. Many new exact traveling wave solutions of the Schamel equation, Schamel-KdV (S-KdV), and the two-dimensional modified KP (Kadomtsev-Petviashvili) equation with square root nonlinearity are constructed. The traveling wave solutions obtained via this method are expressed by hyperbolic functions, the trigonometric functions, and the rational functions. In addition to solitary waves solutions, a variety of special solutions like kink shaped, antikink shaped, and bell type solitary solutions are obtained when the choice of parameters is taken at special values. Two- and three-dimensional plots are drawn to illustrate the nature of solutions. Moreover, the solution obtained via this method is in good agreement with previously obtained solutions of other researchers.

Traveling wave solutions of the one-dimensional Boussinesq paradigm equation

2013 ◽  
Author(s):  
V. M. Vassilev ◽  
P. A. Djondjorov ◽  
M. Ts. Hadzhilazova ◽  
I. M. Mladenov
Keyword(s):  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
One Dimensional ◽  
Wave Solutions ◽  
The One

scholarly journals Lie Group Method for Solving the Negative-Order Kadomtsev–Petviashvili Equation (nKP)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 224
Author(s):  
Ghaylen Laouini ◽  
Amr M. Amin ◽  
Mohamed Moustafa
Keyword(s):  
Lie Group ◽  
Traveling Wave ◽  
Invariant Solution ◽  
Traveling Wave Solutions ◽  
Group Method ◽  
Lie Group Method ◽  
Reduced Equations ◽  
Wave Solutions ◽  
Negative Order ◽  
Petviashvili Equation

A comprehensive study of the negative-order Kadomtsev–Petviashvili (nKP) partial differential equation by Lie group method has been presented. Initially the infinitesimal generators and symmetry reduction, which were obtained by applying the Lie group method on the negative-order Kadomtsev–Petviashvili equation, have been used for constructing the reduced equations. In particular, the traveling wave solutions for the negative-order KP equation have been derived from the reduced equations as an invariant solution. Finally, the extended improved (G′/G) method and the extended tanh method are described and applied in constructing new explicit expressions for the traveling wave solutions. Many new and more general exact solutions are obtained.

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