Similarity reduction and new wave solutions for the 2D stochastic cubic Schrödinger equation with multiplicative white noise arising in optics

In this paper, we have studied the (2+1)-dimensional cubic Schrödinger equation with multiplicative white noise and spatio-temporal dispersion which is considered a model of energy transfer in a monolayer molecular aggregate via the presence of thermal fluctuations and has many applications in optical communications and sensor technology. The direct similarity reduction method is used to find a suitable transformation to reduce the equation to a nonlinear ordinary differential equation (NODE). Then, the reduced NODE is solved by using the F-expansion method because it is an effective method with a wide range of different types of solutions and according to that many different forms of stochastic wave solutions like periodic, kink and bright soliton solutions have been found. The obtained solutions cover solutions yielded before in the literature and also other new ones. Additionally, the different stochastic wave structures have been plotted to differentiate between the deterministic case and the stochastic case. Finally, we can conclude that the two techniques similarity reduction method and the F-expansion method are straightforward and can be applicable to other stochastic partial differential equations.