scholarly journals Travelling Wave Solutions for Two Generalized Hirota-Satsuma Coupled KdV Systems

2001 ◽  
Vol 56 (3-4) ◽  
pp. 312-318 ◽  
Author(s):  
Engui Fan
Keyword(s):  
Full Advantage ◽  
Riccati Equation ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Symbolic Computations ◽  
Extended Tanh Method ◽  
Wave Solutions ◽  
Tanh Method

Abstract In this paper we present an extended tanh method that utilizes symbolic computations to obtain more travelling wave solutions for two generalized Hirota-Satsuma coupled KdV systems in a unified way. The key idea of this method is to take full advantage of a Riccati equation involving a parameter and use its solutions to replace the tanh-function by the tanh method. It is quite interesting that the numbers and types of the traveling wave solutions can be judged from the sign of the parameter. In this paper we investigate the two generalized Hirota-Satsuma coupled KdV systems

scholarly journals Abundant Exact Solition-Like Solutions to the Generalized Bretherton Equation with Arbitrary Constants

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Xiuqing Yu ◽  
Fengsheng Xu ◽  
Lihua Zhang
Keyword(s):  
Full Advantage ◽  
Riccati Equation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions

The Riccati equation is employed to construct exact travelling wave solutions to the generalized Bretherton equation. Taking full advantage of the Riccati equation which has more new solutions, abundant new multiple solition-like solutions are obtained for the generalized Bretherton equation.

scholarly journals Travelling wave solutions for a surface wave equation in fluid mechanics

2016 ◽  
Vol 20 (3) ◽  
pp. 893-898 ◽  
Author(s):  
Yi Tian ◽  
Zai-Zai Yan
Keyword(s):  
Wave Equation ◽  
Fluid Mechanics ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Linear Wave ◽  
Travelling Wave Solutions ◽  
Linear Wave Equation ◽  
Wave Solutions

This paper considers a non-linear wave equation arising in fluid mechanics. The exact traveling wave solutions of this equation are given by using G'/G-expansion method. This process can be reduced to solve a system of determining equations, which is large and difficult. To reduce this process, we used Wu elimination method. Example shows that this method is effective.

scholarly journals Computational and traveling wave analysis of Tzitzéica and Dodd-Bullough-Mikhailov equations: An exact and analytical study

2021 ◽  
Vol 10 (1) ◽  
pp. 272-281
Author(s):  
Hülya Durur ◽  
Asıf Yokuş ◽  
Kashif Ali Abro
Keyword(s):  
Traveling Wave ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Stationary Wave ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Travelling Wave Solutions ◽  
Wave Solutions

Abstract Computational and travelling wave solutions provide significant improvements in accuracy and characterize novelty of imposed techniques. In this context, computational and travelling wave solutions have been traced out for Tzitzéica and Dodd-Bullough-Mikhailov equations by means of (1/G′)-expansion method. The different types of solutions have constructed for Tzitzéica and Dodd-Bullough-Mikhailov equations in hyperbolic form. Moreover, solution function of Tzitzéica and Dodd-Bullough-Mikhailov equations has been derived in the format of logarithmic nature. Since both equations contain exponential terms so the solutions produced are expected to be in logarithmic form. Traveling wave solutions are presented in different formats from the solutions introduced in the literature. The reliability, effectiveness and applicability of the (1/G′)-expansion method produced hyperbolic type solutions. For the sake of physical significance, contour graphs, two dimensional and three dimensional graphs have been depicted for stationary wave. Such graphical illustration has been contrasted for stationary wave verses traveling wave solutions. Our graphical comparative analysis suggests that imposed method is reliable and powerful method for obtaining exact solutions of nonlinear evolution equations.

scholarly journals Lagrangian Formulation, Conservation Laws, Travelling Wave Solutions: A Generalized Benney-Luke Equation

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1480
Author(s):  
Sivenathi Oscar Mbusi ◽  
Ben Muatjetjeja ◽  
Abdullahi Rashid Adem
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Lagrangian Density ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Noether Symmetries ◽  
Extended Tanh Method ◽  
Wave Solutions ◽  
Tanh Method ◽  
Derivatives Of

The aim of this paper is to find the Noether symmetries of a generalized Benney-Luke equation. Thereafter, we construct the associated conserved vectors. In addition, we search for exact solutions for the generalized Benney-Luke equation through the extended tanh method. A brief observation on equations arising from a Lagrangian density function with high order derivatives of the field variables, is also discussed.

scholarly journals Multiple Exact Travelling Solitary Wave Solutions of Nonlinear Evolution Equations

2019 ◽  
pp. 1-13
Author(s):  
M. M. El-Horbaty ◽  
F. M. Ahmed
Keyword(s):  
Riccati Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Travelling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Extended Form ◽  
Wave Solutions ◽  
Tanh Method

An extended Tanh-function method with Riccati equation is presented for constructing multiple exact travelling wave solutions of some nonlinear evolution equations which are particular cases of a generalized equation. The results of solitary waves are general compact forms with non-zero constants of integration. Taking the full advantage of the Riccati equation improves the applicability and reliability of the Tanh method with its extended form.

scholarly journals Exact Traveling Wave Solutions to Benney- Luke Equation

2018 ◽  
Vol 37 ◽  
pp. 1-14
Author(s):  
Zahidul Islam ◽  
Mohammad Mobarak Hossain ◽  
Md Abu Naim Sheikh
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Travelling Wave ◽  
Sobolev Type ◽  
Travelling Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

By using the improved (G¢/G) -expansion method, we obtained some travelling wave solutions of well-known nonlinear Sobolev type partial differential equations, namely, the Benney-Luke equation. We show that the improved (G¢/G) -expansion method is a useful, reliable, and concise method to solve these types of equations.GANIT J. Bangladesh Math. Soc.Vol. 37 (2017) 1-14

scholarly journals Travelling wave solutions for the generalized Schrödinger equation

2021 ◽  
Vol 2090 (1) ◽  
pp. 012062
Author(s):  
G.N. Shaikhova ◽  
B.K. Rakhimzhanov ◽  
Zh.K. Zhanbosinova
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Partial Differential Equations ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Extended Tanh Method ◽  
Physical Problems ◽  
Wave Solutions ◽  
Tanh Method ◽  
Different Types

Abstract In this work, the generalized nonlinear Schrödinger equation is investigated. This equation is integrable and admits Lax pair. To obtain travelling wave solutions the extended tanh method is applied. This method is effective to obtain the exact solutions for different types of nonlinear partial differential equations. Graphs of obtained solutions are presented. The derived solutions are found to be important for the explanation of some practical physical problems.

Travelling Wave Solutions for Generalized Pochhammer-Chree Equations

2002 ◽  
Vol 57 (11) ◽  
pp. 874-882 ◽  
Author(s):  
Biao Li ◽  
Yong Chen ◽  
Hongqing Zhang
Keyword(s):  
Periodic Solutions ◽  
Symbolic Computation ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Rational Solutions ◽  
Extended Tanh Method ◽  
Wave Solutions ◽  
Tanh Method ◽  
Wave Reduction

In this paper, by means of a proper transformation and symbolic computation, we study the travelling wave reduction for the generalized Pochhammer-Chree (PC) equations (1.3) and (1.4) by use of the recently proposed extended-tanh method. As a result, rich travelling wave solutions, which include kink-shaped solitons, bell-shaped solitons, periodic solutions, rational solutions, singular solitons, are obtained. At the same time, using a direct assumption method, the more general bell-shaped solitons for the generalized PC Eq. (1.3) are obtained. The properties of the solutions are show in figures.

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