NEW SOLITARY WAVES OF STOCHASTIC (3+1)-DIMENSIONAL NONLINEAR EVOLUTION EQUATIONS UNDER BROWNIAN MOTION

Abstract

Analysis of nonlinear evolution equations (EEs) arising in soliton theory stems from their fundamental importance in physics and their many implications deepen our understanding of emergent phenomena and nonlinear dynamics. In this paper, we consider two (3 + 1)-dimensional nonlinear EEs that have applications in fluid and plasma physics. The main focus of the paper is to apply the modified tanh method (MTM) which is associated with Riccati equation, to the considered nonlinear EEs. Furthermore, the stochastic dynamics are investigated via adding white noise in terms of Weiner process in the both equations. The results are graphically studied in 3D and 2D, to show the deterministic and stochastic dynamics of different solitary waves.