Variational Perturbation Theory for Fokker-Planck Equation with Nonlinear Drift

TL;DR

This paper introduces a recursive variational perturbation approach to solve the Fokker-Planck equation with nonlinear drift, enabling accurate probability density calculations across all coupling strengths.

Contribution

It presents a novel recursive method combined with variational perturbation theory for solving nonlinear Fokker-Planck equations.

Findings

Series expansion converges exponentially with order

Method accurately predicts probability densities for all coupling values

Comparison with numerical results confirms effectiveness

Abstract

We develop a recursive method for perturbative solutions of the Fokker-Planck equation with nonlinear drift. The series expansion of the time-dependent probability density in terms of powers of the coupling constant is obtained by solving a set of first-order linear ordinary differential equations. Resumming the series in the spirit of variational perturbation theory we are able to determine the probability density for all values of the coupling constant. Comparison with numerical results shows exponential convergence with increasing order.