Variational principles for differential equations with symmetries and conservation laws. I: Second order scalar equations

DOI10.1007/BF01459780zbMath0804.49030MaRDI QIDQ1337548

Juha Pohjanpelto, Ian M. Anderson

Publication date: 9 November 1994

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165205

zbMATH Keywords

inverse problemEuler-Lagrange equationsconservation lawsGelfand-Dickey transformsecond order scalar differential equationssymmetries of a variational problem

Mathematics Subject Classification ID

Variational principles in infinite-dimensional spaces (58E30) Group actions and symmetry properties (58D19) Inverse problems in optimal control (49N45)

Related Items

Variational principles for differential equations with symmetries and conservation laws. II: Polynomial differential equations ⋮ Takens' problem for systems of first order differential equations ⋮ COHOMOLOGY OF LAGRANGE COMPLEXES INVARIANT UNDER PSEUDOGROUPS OF LOCAL TRANSFORMATIONS ⋮ Existence of a variational principle for PDEs with symmetries and current conservation ⋮ Inverse problem on conservation laws ⋮ Symmetries, conservation laws and variational principles for vector field theories† ⋮ Gauge invariance, charge conservation, and variational principles ⋮ Variational principles for natural divergence-free tensors in metric field theories ⋮ The variational sequence on finite jet bundle extensions and the Lagrangian formalism

Cites Work

• Conservation laws of free Klein Gordon fields
• A global version of the inverse problem of the calculus of variations
• The cohomology of invariant variational bicomplexes
• Higher Euler operators and some of their applications
• On the Existence of Global Variational Principles
• Vector-tensor field theories and the Einstein-Maxwell field equations
• ASYMPTOTIC BEHAVIOUR OF THE RESOLVENT OF STURM-LIOUVILLE EQUATIONS AND THE ALGEBRA OF THE KORTEWEG-DE VRIES EQUATIONS
• The Einstein Tensor and Its Generalizations
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