The Exact Solution of the Cauchy Problem for a generalized "linear" vectorial Fokker-Planck Equation - Algebraic Approach

TL;DR

This paper presents an exact algebraic solution to a generalized vectorial Fokker-Planck equation's Cauchy problem, extending Feynman disentangling and Suzuki's methods for broader applications.

Contribution

It introduces a novel algebraic approach that generalizes existing methods to solve vectorial Fokker-Planck equations exactly.

Findings

Exact solution derived for the generalized vectorial Fokker-Planck equation.

Extension of Feynman disentangling techniques to vectorial cases.

Generalization of Suzuki's method for broader classes of equations.

Abstract

The exact solution of the Cauchy problem for a generalized "linear" vectorial Fokker-Planck equation is found using the disentangling techniques of R. Feynman and algebraic (operational) methods. This approach may be considered as a generalization of the Masuo Suzuki's method for solving the 1-dimensional linear Fokker-Planck equation.