The inverse problem of the calculus of variations for scalar fourth-order ordinary differential equations

DOI10.1090/S0002-9947-96-01720-5zbMath0879.34016MaRDI QIDQ5690960

Mark E. Fels

Publication date: 9 January 1997

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

equivalence methoddivergence symmetriesvariational bicomplexinverse problem of the calculus of variationsvariational principles for scalar ordinary differential equations

Mathematics Subject Classification ID

Applications of local differential geometry to the sciences (53B50) Inverse problems involving ordinary differential equations (34A55) Inverse problems in optimal control (49N45)

Related Items (14)

Equivalence conditions and invariants for the general form of Burgers' equations ⋮ A GEOMETRIC SETTING FOR SYSTEMS OF ORDINARY DIFFERENTIAL EQUATIONS ⋮ On the inverse problem of the discrete calculus of variations ⋮ A Hamilton–Jacobi formalism for higher order implicit Lagrangians ⋮ Existence and multiplicity of solutions for a fourth-order differential system with instantaneous and non-instantaneous impulses ⋮ Hamiltonians and conjugate Hamiltonians of some fourth-order nonlinear ODEs ⋮ On Lagrangians and Hamiltonians of some fourth-order nonlinear Kudryashov ODEs ⋮ A Lagrangian description of the higher-order Painlevé equations ⋮ The Quantization of a Fourth-Order Equation without a Second-Order Lagrangian ⋮ The multiplier problem of the calculus of variations for scalar ordinary differential equations ⋮ Equivalence of variational problems of higher order ⋮ Variational Operators, Symplectic Operators, and the Cohomology of Scalar Evolution Equations ⋮ Seeking (and finding) Lagrangians ⋮ Novel Lagrangian hierarchies, generalized variational ODE’s, and families of regular and embedded solitary waves

Cites Work

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• The variational bicomplex for hyperbolic second-order scalar partial differential equations in the plane
• Bäcklund transformations for Darboux integrable differential systems
• The inverse problem of the calculus of variations for ordinary differential equations
• Symmetry bounds of variational problems
• Characteristic Cohomology of Differential Systems (I): General Theory
• Solution of the Inverse Problem of the Calculus of Variations

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