scholarly journals Classical symmetries, travelling wave solutions and conservation laws of a generalized Fornberg–Whitham equation

2017 ◽  
Vol 318 ◽  
pp. 149-155 ◽  
Author(s):  
J.C. Camacho ◽  
M. Rosa ◽  
M.L. Gandarias ◽  
M.S. Bruzón
Keyword(s):  
Conservation Laws ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Classical Symmetries ◽  
Wave Solutions ◽  
Whitham Equation

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 Periodic and Solitary Wave Solutions to the Fornberg-Whitham Equation

2009 ◽  
Vol 2009 ◽  
pp. 1-10 ◽  
Author(s):  
Jiangbo Zhou ◽  
Lixin Tian
Keyword(s):  
Solitary Wave ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Two Parameters ◽  
Whitham Equation

New travelling wave solutions to the Fornberg-Whitham equationut−uxxt+ux+uux=uuxxx+3uxuxxare investigated. They are characterized by two parameters. The expresssions for the periodic and solitary wave solutions are obtained.

Travelling wave solutions of the Fornberg–Whitham equation

2009 ◽  
Vol 215 (8) ◽  
pp. 3068-3075 ◽  
Author(s):  
Aiyong Chen ◽  
Jibin Li ◽  
Xijun Deng ◽  
Wentao Huang
Keyword(s):  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Whitham Equation

scholarly journals On the conservation laws and solutions of a (2+1) dimensional KdV-mKdV equation of mathematical physics

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 211-214 ◽  
Author(s):  
Tanki Motsepa ◽  
Chaudry Masood Khalique
Keyword(s):  
Partial Differential Equations ◽  
Conservation Laws ◽  
Elliptic Functions ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Mkdv Equation ◽  
Jacobi Elliptic Functions ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Physical Phenomena

AbstractIn this paper, we study a (2+1) dimensional KdV-mKdV equation, which models many physical phenomena of mathematical physics. This equation has two integral terms in it. By an appropriate substitution, we convert this equation into two partial differential equations, which do not have integral terms and are equivalent to the original equation. We then work with the system of two equations and obtain its exact travelling wave solutions in form of Jacobi elliptic functions. Furthermore, we employ the multiplier method to construct conservation laws for the system. Finally, we revert the results obtained into the original variables of the (2+1) dimensional KdV-mKdV equation.

Exact Travelling Wave Solutions for the Modified Fornberg-Whitham Equation

2013 ◽  
Vol 14 (1) ◽  
pp. 87-91
Author(s):  
Xijun Deng
Keyword(s):  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Factorization Technique ◽  
Complete Discrimination System ◽  
Whitham Equation

Abstract In this paper, by using the factorization technique combined with the method of complete discrimination system for polynomial, some exact travelling wave solutions for the modified Fornberg-Whitham equation are obtained. Moreover, our results extend previously known results in the literature.

scholarly journals On the Solutions and Conservation Laws of a Coupled Kadomtsev-Petviashvili Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Travelling Wave ◽  
Equation Method ◽  
Travelling Wave Solutions ◽  
Scientific Applications ◽  
Wave Solutions ◽  
Simplest Equation Method ◽  
Petviashvili Equation

A coupled Kadomtsev-Petviashvili equation, which arises in various problems in many scientific applications, is studied. Exact solutions are obtained using the simplest equation method. The solutions obtained are travelling wave solutions. In addition, we also derive the conservation laws for the coupled Kadomtsev-Petviashvili equation.

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