On the geometry of lambda-symmetries, and PDEs reduction

Abstract

We give a geometrical characterization of $\lambda$-prolongations of vector fields, and hence of $\lambda$-symmetries of ODEs. This allows an extension to the case of PDEs and systems of PDEs; in this context the central object is a horizontal one-form $\mu$, and we speak of $\mu$-prolongations of vector fields and $\mu$-symmetries of PDEs. We show that these are as good as standard symmetries in providing symmetry reduction of PDEs and systems, and explicit invariant solutions.

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• On the geometry of lambda-symmetries, and PDEs reduction
• On the relation between standard and $\mu$-symmetries for PDEs
• Partial Lie-point symmetries of differential equations
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Cited by in corpus (20)

• On the geometry of lambda-symmetries, and PDEs reduction
• On the relation between standard and $\mu$-symmetries for PDEs
• Nonlocal aspects of $\lambda$-symmetries and ODEs reduction
• Local and nonlocal solvable structures in ODEs reduction
• Noether theorem for mu-symmetries
• Nonlocal Symmetries, Telescopic Vector Fields and $\lambda$-Symmetries of Ordinary Differential Equations
• Reduction of systems of first-order differential equations via Lambda-symmetries
• ${\mathcal{C}}^{\infty }$-symmetries of distributions and integrability
• A gauge-theoretic description of $\mu$-prolongations, and $\mu$-symmetries of differential equations
• Dynamical systems and σ-symmetries
• Integration of differential equations by ${\mathcal{C}}^{\infty }$-structures
• Solvable structures for evolution PDEs admitting differential constraints
• Symmetry and Lie-Frobenius reduction of differential equations
• Nonlocal interpretation of $\lambda$-variational symmetry-reduction method
• ${\mathcal{C}}^{\infty }$-structures in the integration of involutive distributions
• On the geometry of the Clairin theory of conditional symmetries for higher-order systems of PDEs with applications
• On the Geometry of Twisted Symmetries: Gauging and Coverings
• Lambda-symmetries of Dynamical Systems, Hamiltonian and Lagrangian equations
• Twisted symmetries and integrable systems
• Twisted symmetries of differential equations