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We consider a damped/driven nonlinear Schrodinger equation in an $n$-cube $K^{n}subsetmathbb{R}^n$, $n$ is arbitrary, under Dirichlet boundary conditions [ u_t- uDelta u+i|u|^2u=sqrt{ u}eta(t,x),quad xin K^{n},quad u|_{partial K^{n}}=0, quad u>0, ] where $eta(t,x)$ is a random force that is white in time and smooth in space. It is known that the Sobolev norms of solutions satisfy $ | u(t)|_m^2 le C u^{-m}, $ uniformly in $tge0$ and $ u>0$. In this work we prove that for small $ u>0$ and any initial data, with large probability the Sobolev norms $|u(t,cdot)|_m$ of the solutions with $m>2$ become large at least to the order of $ u^{-kappa_{n,m}}$ with $kappa_{n,m}>0$, on time intervals of order $mathcal{O}(frac{1}{ u})$.
We analyze the energy transfer for solutions to the defocusing cubic nonlinear Schrodinger (NLS) initial value problem on 2D irrational tori. Moreover we complement the analytic study with numerical experimentation. As a biproduct of our investigatio
In this paper we give a new and simplified proof of the theorem on selection of standing waves for small energy solutions of the nonlinear Schrodinger equations (NLS) that we gave in cite{CM15APDE}. We consider a NLS with a Schrodinger operator with
In this article, we prove the scattering for the quintic defocusing nonlinear Schrodinger equation on cylinder $mathbb{R} times mathbb{T}$ in $H^1$. We establish an abstract linear profile decomposition in $L^2_x h^alpha$, $0 < alpha le 1$, motivated
In this paper we study some key effects of a discontinuous forcing term in a fourth order wave equation on a bounded domain, modeling the adhesion of an elastic beam with a substrate through an elastic-breakable interaction. By using a spectral dec
We consider the Cauchy problem for the Gross-Pitaevskii (GP) equation. Using the DBAR generalization of the nonlinear steepest descent method of Deift and Zhou we derive the leading order approximation to the solution of the GP in the solitonic regio