Bifurcation studies, chaotic pattern, phase diagrams and multiple optical solitons for the (2+1)-dimensional stochastic coupled nonlinear Schrödinger system with multiplicative white noise via Itô calculus

The stochastic coupled nonlinear Schrödinger systems are very important equations which can be wildly used in the fields of the optical-fiber communications, nonlinear optics, plasma physics, ecological system, statistical mechanics and so on. This work mainly focuses on dynamical behavior, phase portraits, chaotic behavior and multiple optical solitons for the (2+1)-dimensional stochastic coupled nonlinear Schrödinger system with multiplicative white noise. Here, we analytically deduced bright solitons, dark solitons and periodic solutions through the bifurcation theory. Additionally, some other bounded traveling wave solutions which include Jacobi elliptic function solutions, trigonometric function solutions, rational function solutions, hyperbolic function solutions and solitary wave solutions are also obtained by using the symbolic computation as well as the complete discriminant system method. It is worth noting that we give the classification of all single traveling wave solutions at the same time. Finally, in order to further explore the propagation of the (2+1)-dimensional stochastic coupled nonlinear Schrödinger system in nonlinear optics, three-dimensional, two-dimensional, density graphs and contour graphs are also given.