The current paper is devoted to the stochastic damped higher-order KdV equation driven by white noise. We prove the existence of invariant measure for stochastic damped $(2n+1)$-th order KdV equation with random initial value, and the ergodicity with deterministic initial data.

中文翻译：

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白噪声驱动的随机阻尼高阶KdV方程的遍历性

本文致力于白噪声驱动的随机阻尼高阶KdV方程。我们证明了随机阻尼不变度量的存在$（2ñ+\mathrm{1个}）$具有随机初始值的三阶KdV方程和具有确定性初始数据的遍历性。