Generalized evolutionary equations with imposed symmetries

TL;DR

This paper introduces an algorithm to identify classes of partial differential equations that describe dynamical systems with specific symmetries, demonstrated through Fokker-Planck and Kolmogorov equations.

Contribution

It presents a novel algorithm for deriving generalized evolutionary equations based on symmetry groups and invariants, applicable to various dynamical systems.

Findings

Algorithm successfully identifies symmetry-compatible PDEs

Applied to Fokker-Planck and Kolmogorov equations

Demonstrates the method's effectiveness in specific models

Abstract

The paper proposes an algorithm which could identify a general class of pdes describing dynamical systems with similar symmetries. The way that will be followed starts from a given group of symmetries, the determination of the invariants and, then, of the compatible equations of evolution. The algorithm will be exemplified by two classes of equations which describe the Fokker-Planck model and the "backward" Kolgomorov one.