On the Impact of Noise on Hyperbolic-Type Traveling Wave Solutions of Some Stochastic Evolution Equations

Abstract

In this paper, traveling wave solutions of some nonlinear stochastic evolution equations emerging in miscellaneous fields such as modeling of flame propagation, magneto-acoustic waves in plasma and small-amplitude water waves with surface tension are investigated. By means of Galilean transformation and tanh method, we obtain some exact solutions such as kink wave solution, solitary wave solution and periodic solution. To illustrate the impact of noise on the solutions, we assigned different noise functions for the external noise. The results showed that the waveform deforms as the noise intensity increases.