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Journal of Applied Mathematics
Volume 2012, Article ID 871253, 13 pages
http://dx.doi.org/10.1155/2012/871253
Research Article

Conservation Laws for Some Systems of Nonlinear Partial Differential Equations via Multiplier Approach

Centre for Mathematics and Statistical Sciences, Lahore School of Economics, Lahore 53200, Pakistan

Received 26 July 2012; Accepted 20 September 2012

Academic Editor: Fazal M. Mahomed

Copyright © 2012 Rehana Naz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The conservation laws for the integrable coupled KDV type system, complexly coupled kdv system, coupled system arising from complex-valued KDV in magnetized plasma, Ito integrable system, and Navier stokes equations of gas dynamics are computed by multipliers approach. First of all, we calculate the multipliers depending on dependent variables, independent variables, and derivatives of dependent variables up to some fixed order. The conservation laws fluxes are computed corresponding to each conserved vector. For all understudying systems, the local conservation laws are established by utilizing the multiplier approach.