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 Exact solutions and conservation laws of a coupled integrable dispersionless system

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 957-964 ◽  
Author(s):  
Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Applied Mathematics ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Equation Method ◽  
Lie Symmetry Analysis ◽  
Symmetry Reductions ◽  
Simplest Equation Method ◽  
Mathematics And Physics

In this paper we study the coupled integrable dispersionless system (CIDS), which arises in the analysis of several problems in applied mathematics and physics. Lie symmetry analysis is performed on CIDS and symmetry reductions and exact solutions with the aid of simplest equation method are obtained. In addition, the conservation laws of the CIDS are also derived using the multiplier (and homotopy) approach.

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 and Conservation Laws of a (2+1)-Dimensional Nonlinear KP-BBM Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Khadijo Rashid Adem ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Solitary Waves ◽  
Lie Group ◽  
Group Analysis ◽  
Equation Method ◽  
Two Dimensional ◽  
Lie Group Analysis ◽  
Simplest Equation Method ◽  
Bbm Equation

In this paper, we study the two-dimensional nonlinear Kadomtsov-Petviashivilli-Benjamin-Bona-Mahony (KP-BBM) equation. This equation is the Benjamin-Bona-Mahony equation formulated in the KP sense. We first obtain exact solutions of this equation using the Lie group analysis and the simplest equation method. The solutions obtained are solitary waves. In addition, the conservation laws for the KP-BBM equation are constructed by using the multiplier method.

The new exact solutions of the new coupled Konno-Oono equation by using extended simplest equation method

2018 ◽  
Vol 12 (6) ◽  
pp. 293-301 ◽  
Author(s):  
Montri Torvattanabun ◽  
Papraporn Juntakud ◽  
Adsadawut Saiyun ◽  
Nattawut Khansai
Keyword(s):  
Exact Solutions ◽  
Equation Method ◽  
New Exact Solutions ◽  
Simplest Equation Method

scholarly journals Exact Solutions for a New Nonlinear KdV-Like Wave Equation Using Simplest Equation Method and Its Variants

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Yinghui He ◽  
Yun-Mei Zhao ◽  
Yao Long
Keyword(s):  
Thin Film ◽  
Wave Equation ◽  
Exact Solutions ◽  
Wave Motion ◽  
Wave Equations ◽  
Equation Method ◽  
Nonlinear Wave Equations ◽  
New Exact Solutions ◽  
Simplest Equation Method ◽  
Film Mass Transfer

The simplest equation method presents wide applicability to the handling of nonlinear wave equations. In this paper, we focus on the exact solution of a new nonlinear KdV-like wave equation by means of the simplest equation method, the modified simplest equation method and, the extended simplest equation method. The KdV-like wave equation was derived for solitary waves propagating on an interface (liquid-air) with wave motion induced by a harmonic forcing which is more appropriate for the study of thin film mass transfer. Thus finding the exact solutions of this equation is of great importance and interest. By these three methods, many new exact solutions of this equation are obtained.

scholarly journals The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Yun-Mei Zhao ◽  
Ying-Hui He ◽  
Yao Long
Keyword(s):  
Exact Solutions ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Equation Method ◽  
Simplest Equation Method ◽  
Klein Gordon ◽  
Schrödinger's Equation ◽  
Wave Reduction

A good idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the elliptic-like equations are derived using the simplest equation method and the modified simplest equation method, and then the exact solutions of a class of nonlinear evolution equations which can be converted to the elliptic-like equation using travelling wave reduction are obtained. For example, the perturbed nonlinear Schrödinger’s equation (NLSE), the Klein-Gordon-Zakharov (KGZ) system, the generalized Davey-Stewartson (GDS) equations, the Davey-Stewartson (DS) equations, and the generalized Zakharov (GZ) equations are investigated and the exact solutions are presented using this method.

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