In this paper, we introduce the concept of stochastic bifurcations of group-invariant solutions for stochastic nonlinear wave equations. The essence of this concept is to display bifurcation phenomena by investigating stochastic P-bifurcation and stochastic D-bifurcation of stochastic ordinary differential equations derived by Lie symmetry reductions of stochastic nonlinear wave equations. Stochastic bifurcations of group-invariant solutions can be considered as an indirect display of bifurcation phenomena of stochastic nonlinear wave equations. As a constructive example, we study stochastic bifurcations of group-invariant solutions for a generalized stochastic Zakharov–Kuznetsov equation.

中文翻译：

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广义随机 Zakharov-Kuznetsov 方程组不变解的随机分岔

在本文中，我们介绍了随机非线性波动方程组不变解的随机分岔的概念。这个概念的本质是通过研究随机非线性波动方程的李对称约简得到的随机常微分方程的随机 P 分岔和随机 D 分岔来显示分岔现象。群不变解的随机分岔可以看作是随机非线性波动方程分岔现象的间接表现。作为一个建设性的例子，我们研究了广义随机 Zakharov-Kuznetsov 方程的群不变解的随机分岔。