Phase characterization and optical solitons for the stochastic nonlinear Schr?dinger equation with multiplicative white noise and spatio-temporal dispersion via It? calculus

The main purpose of this work focuses on studying dynamical behavior and optical soliton solutions for the stochastic nonlinear Schrodinger equation with multiplicative white noise and spatio-temporal dispersion. Here, we analytically construed periodic wave solutions, bell -shaped solitary wave solutions and kink-shaped solitary wave solutions via the bifurcation theory of dynamical system. What is more, with the assistance of the complete discriminant system method and symbolic computation, a range of new optical soliton solutions have been derived, which include some families of Jacobian elliptic function solutions, rational function solutions and implicit analytical solutions. It is worth finding that the obtained optical solitons in this paper substantially improve the corresponding results in the known literature. Finally, we give the comparison between our solutions and other's results.