Conservation Laws for a Variable Coefficient Variant Boussinesq System

Conservation Laws for a Variable Coefficient Variant Boussinesq System

We construct the conservation laws for a variable coefficient variant Boussinesq system, which is a third-order system of two partial differential equations. This system does not have a Lagrangian and so we transform it to a system of fourth-order, which admits a Lagrangian. Noether’s approach is th...

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Main Authors: Ben Muatjetjeja, Chaudry Masood Khalique
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/169694
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spelling doaj-9b686a4578a04b558dfcee4bc482ad4f2020-11-25T00:33:46ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/169694169694Conservation Laws for a Variable Coefficient Variant Boussinesq SystemBen Muatjetjeja0Chaudry Masood Khalique1Department of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South AfricaDepartment of Mathematical Sciences, International Institute for Symmetry Analysis and Mathematical Modelling, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South AfricaWe construct the conservation laws for a variable coefficient variant Boussinesq system, which is a third-order system of two partial differential equations. This system does not have a Lagrangian and so we transform it to a system of fourth-order, which admits a Lagrangian. Noether’s approach is then utilized to obtain the conservation laws. Lastly, the conservation laws are presented in terms of the original variables. Infinite numbers of both local and nonlocal conserved quantities are derived for the underlying system.http://dx.doi.org/10.1155/2014/169694
collection DOAJ
language English
format Article
sources DOAJ
author Ben Muatjetjeja
Chaudry Masood Khalique
spellingShingle Ben Muatjetjeja
Chaudry Masood Khalique
Conservation Laws for a Variable Coefficient Variant Boussinesq System
Abstract and Applied Analysis
author_facet Ben Muatjetjeja
Chaudry Masood Khalique
author_sort Ben Muatjetjeja
title Conservation Laws for a Variable Coefficient Variant Boussinesq System
title_short Conservation Laws for a Variable Coefficient Variant Boussinesq System
title_full Conservation Laws for a Variable Coefficient Variant Boussinesq System
title_fullStr Conservation Laws for a Variable Coefficient Variant Boussinesq System
title_full_unstemmed Conservation Laws for a Variable Coefficient Variant Boussinesq System
title_sort conservation laws for a variable coefficient variant boussinesq system
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description We construct the conservation laws for a variable coefficient variant Boussinesq system, which is a third-order system of two partial differential equations. This system does not have a Lagrangian and so we transform it to a system of fourth-order, which admits a Lagrangian. Noether’s approach is then utilized to obtain the conservation laws. Lastly, the conservation laws are presented in terms of the original variables. Infinite numbers of both local and nonlocal conserved quantities are derived for the underlying system.
url http://dx.doi.org/10.1155/2014/169694
work_keys_str_mv AT benmuatjetjeja conservationlawsforavariablecoefficientvariantboussinesqsystem
AT chaudrymasoodkhalique conservationlawsforavariablecoefficientvariantboussinesqsystem
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