Stochastic Analysis and White Noise Calculus of Nonlinear Wave Equations with Application to Laser Propagation and Generation

TL;DR

This paper develops a unified mathematical framework for analyzing nonlinear stochastic wave equations relevant to laser physics and random media, employing Ito and white noise calculus to establish solution existence and uniqueness.

Contribution

It introduces a comprehensive abstract framework for nonlinear stochastic wave equations and applies advanced stochastic calculus methods to prove solution properties.

Findings

Established existence and uniqueness of mild solutions.

Unified treatment of various laser and wave propagation models.

Applied white noise calculus to complex stochastic wave equations.

Abstract

In this paper we study a large class of nonlinear stochastic wave equations that arise in laser generation models and models for propagation in random media in a unified mathematical framework. Continuous and pulse-wave propagation models, free electron laser generation models, as well as laser-plasma interaction models have been cast in a convenient and unified abstract framework as semilinear evolution equations in a Hilbert space to enable stochastic analysis. We formulate Ito calculus and white noise calculus methods of treating stochastic terms and prove existence and uniqueness of mild solutions.