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 Exact Solutions ofϕ4Equation Using Lie Symmetry Approach along with the Simplest Equation and Exp-Function Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Hossein Jafari ◽  
Nematollah Kadkhoda ◽  
Chaudry Masood Khalique
Keyword(s):  
Exact Solutions ◽  
Function Method ◽  
Travelling Wave ◽  
Lie Symmetry ◽  
Equation Method ◽  
Travelling Wave Solutions ◽  
Symmetry Approach ◽  
Wave Solutions ◽  
Simplest Equation Method ◽  
Lie Symmetry Approach

This paper obtains the exact solutions of theϕ4equation. The Lie symmetry approach along with the simplest equation method and the Exp-function method are used to obtain these solutions. As a simplest equation we have used the equation of Riccati in the simplest equation method. Exact solutions obtained are travelling wave solutions.

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 Exact Explicit Solutions and Conservation Laws for a Coupled Zakharov-Kuznetsov System

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Equation Method ◽  
Explicit Solutions ◽  
Simplest Equation Method ◽  
De Vries

We study a coupled Zakharov-Kuznetsov system, which is an extension of a coupled Korteweg-de Vries system in the sense of the Zakharov-Kuznetsov equation. Firstly, we obtain some exact solutions of the coupled Zakharov-Kuznetsov system using the simplest equation method. Secondly, the conservation laws for the coupled Zakharov-Kuznetsov system will be constructed by using the multiplier approach.

scholarly journals Travelling Wave Solutions of the Perturbed Wadati-Segur-Ablowitz Equation by (G'/G)-Expansion Method

2018 ◽  
Vol 6 (06) ◽  
Author(s):  
Figen Kangalgil
Keyword(s):  
Exact Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena

The investigation of the exact solutions of NLPDEs plays an im- portant role for the understanding of most nonlinear physical phenomena. Also, the exact solutions of this equations aid the numerical solvers to assess the correctness of their results. In this paper, (G'/G)-expansion method is pre- sented to construct exact solutions of the Perturbed Wadati-Segur-Ablowitz equation. Obtained the exact solutions are expressed by the hyperbolic, the trigonometric and the rational functions. All calculations have been made with the aid of Maple program. It is shown that the proposed algorithm is elemen- tary, e¤ective and has been used for many PDEs in mathematical physics.  

Bright soliton solutions, power series solutions and travelling wave solutions of a (3+1)-dimensional modified Korteweg–de Vries–Kadomtsev–Petviashvili equation

2018 ◽  
Vol 32 (06) ◽  
pp. 1850082
Author(s):  
Ding Guo ◽  
Shou-Fu Tian ◽  
Li Zou ◽  
Tian-Tian Zhang
Keyword(s):  
Power Series ◽  
Soliton Solutions ◽  
Travelling Wave ◽  
Bright Soliton ◽  
Travelling Wave Solutions ◽  
Series Solutions ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
Power Series Solutions ◽  
De Vries

In this paper, we consider the (3[Formula: see text]+[Formula: see text]1)-dimensional modified Korteweg–de Vries–Kadomtsev–Petviashvili (mKdV-KP) equation, which can be used to describe the nonlinear waves in plasma physics and fluid dynamics. By using solitary wave ansatz in the form of sech[Formula: see text] function and a direct integrating way, we construct the exact bright soliton solutions and the travelling wave solutions of the equation, respectively. Moreover, we obtain its power series solutions with the convergence analysis. It is hoped that our results can provide the richer dynamical behavior of the KdV-type and KP-type equations.

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