Stochastic Process Associated with Traveling Wave Solutions of the Sine-Gordon Equation

TL;DR

This paper introduces stochastic processes linked to traveling wave solutions of the sine-Gordon equation, analyzing their structure and behavior through numerical methods and providing an interpretation based on the equation of motion.

Contribution

It presents a novel connection between stochastic processes and traveling wave solutions of the sine-Gordon equation, emphasizing the role of the forward Kolmogorov equation as a conservation law.

Findings

Numerical analysis of the stochastic processes

Interpretation of process behaviors via equations of motion

Structural insights into the Kolmogorov equation as a conservation law

Abstract

Stochastic processes associated with traveling wave solutions of the sine-Gordon equation are presented. The structure of the forward Kolmogorov equation as a conservation law is essential in the construction and so is the traveling wave structure. The derived stochastic processes are analyzed numerically. An interpretation of the behaviors of the stochastic processes is given in terms of the equation of motion.