General mechanism of invariant reduction and Noether's theorem

Abstract: Given a local (point, contact, or higher) symmetry of a system of partial differential equations, one can consider the system that describes the invariant solutions (the invariant system). It seems natural to expect that the invariant system inherits symmetry-invariant geometric structures in a specific way. We propose a mechanism of reduction of symmetry-invariant geometric structures, which relates them to their counterparts on the respective invariant systems. This mechanism covers conservation laws, the stationary action principle, presymplectic structures, and more. In particular, a version of Noether's theorem naturally arises for systems that describe invariant solutions.

This is joint work with A. Cheviakov.

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsnumerical analysisexactly solvable and integrable systemsfluid dynamics

Audience: researchers in the topic

Mathematical models and integration methods