Investigation of nonlinear problems governed by stochastic phi-4 type equations in nuclear and particle physics

Abstract

In this article, the stochastic Phi-4 model is under consideration analytically. The stochastic Phi-4 equation has been crucial to nuclear and particle physics. The randomness of the nuclear particle at the micro level represented by the stochastic phenomena which are shown by the white noise. The stochastic version of the Phi-4 model is investigated for the first time analytically to gain the soliton solutions by using the two techniques such as Sardar sub-equation and modified exponential rational function. The stochastic soliton solutions are successfully constructed in the form of exponential, trigonometric, and hyperbolic forms. Additionally, the stability analysis of this model is observed. Lastly, the stochastic behavior of some solutions is shown in the form of 2D, and 3D by choosing the different values of parameters.