The geometry of differential constraints for a class of evolution PDEs

Abstract

The problem of computing differential constraints for a family of evolution PDEs is discussed from a constructive point of view. A new method, based on the existence of generalized characteristics for evolution vector fields, is proposed in order to obtain explicit differential constraints for PDEs belonging to this family. Several examples, with applications in non-linear stochastic filtering theory, stochastic perturbation of soliton equations and non-isospectral integrable systems, are discussed in detail to verify the effectiveness of the method.

Revised abstract and introduction

References in corpus (6)

• Variational Principles for Stochastic Fluid Dynamics
• Variational Principles for Stochastic Soliton Dynamics
• Momentum Maps and Stochastic Clebsch Action Principles
• Affine realizations with affine state processes for stochastic partial differential equations
• Solvable structures for evolution PDEs admitting differential constraints
• Finite dimensional solutions to SPDEs and the geometry of infinite jet bundles

Cited by in corpus (4)

• Symmetries of Stochastic Differential Equations using Girsanov transformations
• Weak symmetries of stochastic differential equations driven by semimartingales with jumps
• Noether theorem in stochastic optimal control problems via contact symmetries
• Symmetries and invariance properties of stochastic differential equations driven by semimartingales with jumps