Exact solutions of equation for description of embedded solitons

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

“…In [11], Han et al studied the exact solutions and bifurcation of the stochastic fractional long-short wave equation by using the dynamical system method. In [12], Zayed et al obtained the dispersive optical solitons of stochastic perturbed generalized Schrödinger-Hirota equation by the extended simplest equation algorithm and the Φ 6 -model expansion method. In [13], He and Wang studied the soliton solutions of stochastic nonlinear Schrödinger equation using the bilinear method.…”

“…Generally, ES [2][3][4] is a new type of solitary waves, which exists in the continuous spectrum of the nonlinear wave system and is limited in the continuous spectrum of the nonlinear system [5][6][7]. ESs are usually used 5 to describe the solutions of nonlinear partial differential equations from hydrodynamics, nonlinear optics and liquid crystal theory [8][9][10].…”

Dynamics and Embedded Solitons of Stochastic Quadratic and Cubic Nonlinear Susceptibilities with Multiplicative White Noise in the Itô Sense

“…After that, Yang et al [1] found ESs in a continuous model, an unstable model and a discrete model, and further explained ESs. Generally, the ES [2][3][4] is a new type of solitary wave, which exists in the continuous spectrum of a nonlinear wave system and is limited in the continuous spectrum of a nonlinear system [5][6][7]. ESs are usually used to describe the solutions of nonlinear partial differential equations from hydrodynamics, nonlinear optics and liquid crystal theory [8][9][10][11].…”