Dynamics and embedded solitons of stochastic quadratic χ(2) and cubic χ(3) nonlinear susceptibilities with multiplicative white noise in the Itô sense

Abstract

The main purpose of this paper is to study the dynamics and embedded solitons of stochastic quadratic χ(2) and cubic χ(3) nonlinear susceptibilities in the Itˆo sense. Firstly, two-dimensional dynamics system and its perturbation system are obtained by using travelling wave transformation. Secondly, phase portraits of two-dimensional dynamics system are plotted. What’s more, chaotic behaviors, two-dimensional phase portraits, three-dimensional phase portraits and sensitivity of the perturbation system are analyzed by using the Maple software. Finally, the embedded solitons of stochastic quadratic χ(2) and cubic χ(3) nonlinear susceptibilities are obtained. Moreover, three-dimensional and two-dimension of stochastic quadratic χ(2) and cubic χ(3) nonlinear susceptibilities are plotted.