Construction of the first-order stochastic nonlinear differential equations in the modeling of stimulated scattering of optical fields

Abstract

In this work we use a technique inspired by the inverse problem in the scattering theory, that is, the calculation of partial derivatives along the characteristic directions of the D'Alembert solution of the wave equation (Maxwell and Euler). In this way, we construct a system of stochastic non-linear differential equations. The analysis of this system, using algebraic invariants, gives more information in comparison with that given by Ghelfand-Levitan-Marcenko, in the inverse problem in the scattering theory.