Exact travelling wave solutions to the two-dimensional stochastic Allen-Cahn equation with multiplicative noise are obtained through the hyperbolic tangent (tanh) method. This technique limits the solutions to travelling wave profiles by representing them with a finite tanh power series. This study focuses on how multiplicative noise affects the dynamics of these travelling waves, in particular, occurring of wave propagation failure due to high levels of noise.

翻译：通过双曲正切（tanh）方法，获得了带有乘性噪声的二维随机Allen-Cahn方程的精确行波解。该方法通过将解表示为有限阶tanh幂级数的形式，将解限定为行波剖面。本研究重点分析乘性噪声对行波动力学行为的影响，特别是高噪声水平下可能导致波传播失效的现象。