The exact solutions of the stochastic Ginzburg-Landau equation

The main goal of this paper is to obtain the exact solutions of the stochastic real-valued Ginzburg-Landau equation, which is forced by multiplicative noise in the Ito? sense. It is necessary to get the exact solutions of this equation because it occurs in numerous fields of physics, mathematics and chemistry. We use three different methods such as the tanh-coth, the Riccati-Bernoulli sub-ODE and the generalized G-/G-expansion methods in order to obtain a new trigonometric and hyperbolic stochastic solutions. The main advantage of these three methods is their applicability in solving similar models. The novelty of the present paper is that the results obtained here extend and improve some results that were previously obtained. Moreover, we plot 3D surfaces of analytical solutions obtained in this paper by using Matlab to illustrate the impact of multiplicative noise on the solutions of the stochastic real-valued Ginzburg-Landau equation.

Automated summary

The paper aims to obtain exact solutions of the stochastic real-valued Ginzburg-Landau equation forced by multiplicative noise, using three different methods to derive new trigonometric and hyperbolic stochastic solutions. The novelty lies in extending and improving previous results, and 3D surfaces of analytical solutions are plotted using Matlab to illustrate the impact of multiplicative noise on the equation's solutions.