On travelling-wave solutions to systems of conservation laws with singular viscosity

1987 ◽  
Vol 12 (11) ◽  
pp. 1285-1307 ◽  
Author(s):  
Howard Prue ◽  
Richard Sanders
Keyword(s):  
Conservation Laws ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Systems Of Conservation Laws

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 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.

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.

scholarly journals Conservation Laws and Travelling Wave Solutions for Double Dispersion Equations in (1+1) and (2+1) Dimensions

2020 ◽  
Author(s):  
Maria Luz Gandarias ◽  
Maria Rosa Duran ◽  
Chaudry Masood khalique
Keyword(s):  
Conservation Laws ◽  
Dispersion Equation ◽  
Nonlinear Wave ◽  
Travelling Waves ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Dispersion Equations ◽  
Wave Solutions ◽  
Double Dispersion ◽  
Long Nonlinear Wave

In this article, we investigate two types of double dispersion equations in two dierent dimensions. Double dispersion equation were derived to describe long nonlinear wave evolution in a thin hyperelastic rod. Conservation laws are obtained for these equations by the application of the multiplier method. Finally, travelling waves and line travelling waves are respectively considered for these two equations.

Solitary and Travelling Wave Solutions of Certain Nonlinear Diffusion-Reaction Equations

2020 ◽  
Author(s):  
Miftachul Hadi
Keyword(s):  
Nonlinear Diffusion ◽  
Travelling Wave ◽  
Diffusion Reaction ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Reaction Equations

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.

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