Nonlinear Dynamics

, Volume 36, Issue 1, pp 29–40 | Cite as

Lagrangian Approach to Evolution Equations: Symmetries and Conservation Laws

Article

Abstract

We show that one can apply a Lagrangian approach to certain evolution equations by considering them together with their associated equations. Consequently, one can employ Noether's theorem and derive conservation laws from symmetries of coupled systems of evolution equations. We discuss in detail the linear and non-linear heat equations as well as the Burgers equation and obtain new non-local conservation laws for the non-linear heat and the Burgers equations by extending their symmetries to the associated equations. We also provide Lagrangians for non-linear Schrödinger and Korteweg—de Vries type systems.

conservation laws evolution equations Lagrangians for extended systems symmetries 

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Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  1. 1.Research Centre ALGA: Advances in Lie Group Analysis, Department of Health, Science and MathematicsBlekinge Institute of TechnologyKarlskronaSweden
  2. 2.Department of MathematicsRoyal Institute of TechnologyStockholmSweden

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