Extended symmetry analysis of a "nonconservative Fokker-Plank equation"

TL;DR

This paper extends the symmetry analysis of a nonconservative Fokker-Planck equation by leveraging its reduction to the linear heat equation, providing a comprehensive description of symmetries and conservation laws.

Contribution

It offers a systematic derivation of symmetries and conservation laws for the equation using known results from the heat equation, including nonclassical symmetries and potential conservation laws.

Findings

All symmetries and conservation laws can be derived from the heat equation results.

Exhaustive description of nonclassical symmetries and conservation laws.

Construction of infinite series of potential symmetry algebras.

Abstract

We show that all results of Yasar and Ozer [Comput. Math. Appl. 59 (2010), 3203-3210] on symmetries and conservation laws of a "nonconservative Fokker-Planck equation" can be easily derived from results existing in the literature by means of using the fact that this equation is reduced to the linear heat equation by a simple point transformation. Moreover nonclassical symmetries and local and potential conservation laws of the equation under consideration are exhaustively described in the same way as well as infinite series of potential symmetry algebras of arbitrary potential orders are constructed.