Embedded solitons, chaotic behavior, bifurcation of cubic-quartic χ(2) and χ(3) nonlinear susceptibilities with multiplicative white noise

The main objective of this paper is to study the chaotic behavior and embedded soliton of cubic-quartic χ(2) and χ(3) nonlinear susceptibilities with multiplicative white noise. Firstly, traveling wave transformation and the trial equation method are used to obtain the nonlinear ordinary differential equations. Secondly, chaotic behavior, bifurcation and sensitivity of the perturbed perturbation system are studied. Thirdly, the embedded soliton solutions of cubic-quartic χ(2) and cubic χ(3) nonlinear model can be obtained.