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Lagrangian approach to evolution equations: Symmetries and conservation laws
KTH, Superseded Departments, Mathematics.
2004 (English)In: Nonlinear dynamics, ISSN 0924-090X, E-ISSN 1573-269X, Vol. 36, no 1, 29-40 p.Article in journal (Refereed) Published
Abstract [en]

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 Schrodinger and Korteweg-de Vries type systems.

Place, publisher, year, edition, pages
2004. Vol. 36, no 1, 29-40 p.
Keyword [en]
conservation laws, evolution equations, Lagrangians for extended systems, symmetries
National Category
Applied Mechanics
URN: urn:nbn:se:kth:diva-23568DOI: 10.1023/B:NODY.0000034644.82259.1fISI: 000222611300004ScopusID: 2-s2.0-3242777900OAI: diva2:342266
QC 20100525 QC 20111028Available from: 2010-08-10 Created: 2010-08-10 Last updated: 2011-10-28Bibliographically approved

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ReferencesLink to record
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