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math.DS2013
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…
math.DS2013
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…
math.DS2013★ 1 cited
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…