We establish a new criterion for exponential mixing of random dynamical systems. Our
criterion is applicable to a wide range of systems, including in particular dispersive …

The current paper is devoted to the asymptotic behavior of stochastic modified Korteweg–de
Vries equation with fractional dissipation. Firstly, based on estimates to trilinear term and …

This paper presents the support set and unique ergodicity of invariant measure given in
Ekren (2018) of stochastic KdV equation, which also offers an answer to the question about …

The current paper is devoted to stochastic damped higher order KdV equation driven by
Poisson process. We establish the well-posedness of stochastic damped higher-order KdV …

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 (2 n+ 1)-th …

The current paper is devoted to the stochastic damped Ostrovsky equation driven by white
noise. By establishing the uniform estimates for the solution in norm, we prove the global …

This paper is devoted to the stochastic damped Ostrovsky equation driven by pure jump
noise. The uniformly bounded of solutions in H1 (R) and L2 (R) space are established …

We address the long-time behavior of solutions to damped dispersive stochastic partial
differential equations, namely the KdV equation and the nonlinear Schrödinger equation on …