The Jacobi elliptic function method and its application for the stochastic NNV system

In this paper, the stochastic Nizhnik-Novikov-Veselov (NNV) system, which is a two-dimensional with a multiplicative noise in the Ito sense is studied for simple periodic wave solutions. The obtained stochastic solutions of the (2+1)-dimensional stochastic NNV system may be used to investigate the sound waves in any stochastic system. Here, the Jacobi elliptic function (JEF) approach is used to obtain the periodic wave solutions, and it is noted that the solutions are determined in terms of trigonometric, hyperbolic, and rational functions. By using some special values of the parameters, we show that the graphically obtained solutions include soliton solutions such as double periodic waves, shock wave solutions or kink-shaped soliton solutions, solitary waves or bell-shape solitons, and periodic wave solutions, all of which are included in the concluding section of this paper. These solutions are novel and are reported for the first time in the study of the stochastic NNV system.