An analysis to extract the soliton solutions for the Lonngren wave equation and the (2+1)-dimensional stochastic Nizhnik-Novikov-Veselov system

Abstract In this research article, we have extracted simple closed form resolutions containing the variables and some parameters of the Lonngren wave equation and the (2 + 1)-dimensional stochastic Nizhnik-Novikov-Veselov system pressed in the Ito sense by augmentative noise. The acquired solutions of the Lonngren wave equation and the (2 + 1)-dimensional stochastic Nizhnik-Novikov-Veselov system may be effective to explore the electromagnetic signals in any cable lines and sound wave in any stochastic system respectively. For the required solutions, we use here the two variables (G1⁄G, 1/G)-expansion method and we notice the obtained solutions are ascertained in terms of trigonometric function, hyperbolic function, and rational function types. By taking the parameters as some special values, we see that the obtained solutions graphically imply the soliton solutions like as, singular solition, singular periodic solution, bell shape soliton and anti-bell shape soliton which all are added in the ultimate part of this paper.