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Nonlinear Dynamics

, Volume 61, Issue 1–2, pp 217–228 | Cite as

Approximate conservation laws of perturbed partial differential equations

  • Yani Gan
  • Changzheng Qu
Original Paper

Abstract

This paper presents a general result on approximate conservation laws of perturbed partial differential equations. A method of constructing approximate conservation laws to systems of perturbed partial differential equations is given, which is based on approximate Noether symmetries of approximate and standard adjoint systems of the original system. The relationship between the Noether symmetry operators of approximate and standard adjoint system is established. As a result, the approach is applied to the perturbed wave equation and the perturbed KdV equation.

Conservation law Lagrangian Noether symmetry Adjoint system 

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Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Center for Nonlinear StudiesNorthwest UniversityXi’anChina
  2. 2.Department of MathematicsNorthwest UniversityXi’anChina

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