13 citations · 17 across the 10 of their papers we have counts for
12 papers
Averaging for stochastic perturbations of integrable systems
Guan Huang, Sergei Kuksin, Andrey Piatnitski
We are concerned with averaging theorems for -small stochastic perturbations of integrable equations in $$ \dot I(t) =0,\quad \dot…
Averaging and mixing for stochastic perturbations of linear conservative systems
Guan Huang, Sergei Kuksin
We study stochastic perturbations of linear systems of the form where is a linear operator with n…
On averaging and mixing for stochastic PDEs
Guan Huang, Sergei Kuksin
We examine the convergence in the Krylov--Bogolyubov averaging for nonlinear stochastic perturbations of linear PDEs with pure imaginary spectrum and show that if the involved effe…
On The Energy Transfer To High Frequencies In The Damped/Driven Nonlinear Schrödinger Equation (Extended Version)
Guan Huang, Sergei Kuksin
We consider a damped/driven nonlinear Schrödinger equation in an -cube , is arbitrary, under Dirichlet boundary conditions \[ u_t-νΔu+i|u|^2u=\sqrt…
On the finite dimensionality of integrable deformations of strictly convex integrable billiard tables
Guan Huang, Vadim Kaloshin
In this paper, we show that any smooth one-parameter deformations of a strictly convex integrable billiard table preserving the integrability near the boundary have to be tan…
Nearly circular domains which are integrable close to the boundary are ellipses
Guan Huang, Vadim Kaloshin, Alfonso Sorrentino
The Birkhoff conjecture says that the boundary of a strictly convex integrable billiard table is necessarily an ellipse. In this article, we consider a stronger notion of integrabi…
On the Marked Length Spectrums of Generic Strictly Convex Billiard Tables
Guan Huang, Vadim Kaloshin, Alfonso Sorrentino
In this paper we show that for a generic strictly convex domain, one can recover the eigendata corresponding to Aubry-Mather periodic orbits of the induced billiard map, from the (…
Time-averaging for weakly nonlinear CGL equations with arbitrary potentials
Guan Huang, Sergei Kuksin, Alberto Maiocchi
Consider weakly nonlinear complex Ginzburg--Landau (CGL) equation of the form: under the periodic boundary…
Long-time dynamics of resonant weakly nonlinear CGL equations
Guan Huang
Consider a weakly nonlinear CGL equation on the torus~: \[u_t+iΔu=ε[μ(-1)^{m-1}Δ^{m} u+b|u|^{2p}u+ ic|u|^{2q}u].\eqno{(*)}\] Here , , $0<ε…
An averaging theorem for nonlinear Schrödinger equations with small nonlinearities
Guan Huang
Consider nonlinear Schrödinger equations with small nonlinearities \[\frac{d}{dt}u+i(-\triangle u+V(x)u)=ε\mathcal{P}(\triangle u,u,x),\quad x\in \mathbb{T}^d.\eqno{(*)}\] Let $\{ζ…
On long time dynamics of perturbed KdV equations
Guan Huang
Consider perturbed KdV equations: \[u_t+u_{xxx}-6uu_x=εf(u(\cdot)),\quad x\in\mathbb{T}=\mathbb{R}/\mathbb{Z},\;\int_{\mathbb{T}}u(x,t)dx=0,\] where the nonlinearity defines analyt…
An Averaging Theorem for Perturbed KdV Equation
Guan Huang
We consider a perturbed KdV equation: [\dot{u}+u_{xxx} - 6uu_x = εf(x,u(\cdot)), \quad x\in \mathbb{T}, \quad\int_\mathbb{T} u dx=0.] For any periodic function , let $I(u)=(I…