On the relation between standard and $\mu$-symmetries for PDEs

Abstract

We give a geometrical interpretation of the notion of $\mu$-prolongations of vector fields and of the related concept of $\mu$-symmetry for partial differential equations (extending to PDEs the notion of $\lambda$-symmetry for ODEs). We give in particular a result concerning the relationship between $\mu$-symmetries and standard exact symmetries. The notion is also extended to the case of conditional and partial symmetries, and we analyze the relation between local $\mu$-symmetries and nonlocal standard symmetries.

25 pages, no figures, latex. to be published in J. Phys. A

References in corpus (5)

• On the Differential Geometry of $G{L}_q(1|1)$
• On the geometry of lambda-symmetries, and PDEs reduction
• Partial Lie-point symmetries of differential equations
• Weak Transversality and Partially Invariant Solutions
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Cited by in corpus (14)

• On the geometry of lambda-symmetries, and PDEs reduction
• Nonlocal aspects of $\lambda$-symmetries and ODEs reduction
• Local and nonlocal solvable structures in ODEs reduction
• Noether theorem for mu-symmetries
• Reduction of systems of first-order differential equations via Lambda-symmetries
• A generalization of λ-symmetry reduction for systems of ODEs: σ-symmetries
• ${\mathcal{C}}^{\infty }$-symmetries of distributions and integrability
• A gauge-theoretic description of $\mu$-prolongations, and $\mu$-symmetries of differential equations
• Dealing with Rational Second Order Ordinary Differential Equations where both Darboux and Lie Find It Difficult: The $S$-function Method
• Dynamical systems and σ-symmetries
• Integration of differential equations by ${\mathcal{C}}^{\infty }$-structures
• Symmetry and Lie-Frobenius reduction of differential equations
• ${\mathcal{C}}^{\infty }$-structures in the integration of involutive distributions
• On the Geometry of Twisted Symmetries: Gauging and Coverings