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This paper deals with the 2-D Schrodinger equation with time-oscillating exponential nonlinearity $ipartial_t u+Delta u= theta(omega t)big(e^{4pi|u|^2}-1big)$, where $theta$ is a periodic $C^1$-function. We prove that for a class of initial data $u_0 in H^1(mathbb{R}^2)$, the solution $u_{omega}$ converges, as $|omega|$ tends to infinity to the solution $U$ of the limiting equation $ipartial_t U+Delta U= I(theta)big(e^{4pi|U|^2}-1big)$ with the same initial data, where $I(theta)$ is the average of $theta$.
We investigate the invariance of the Gibbs measure for the fractional Schrodinger equation of exponential type (expNLS) $ipartial_t u + (-Delta)^{frac{alpha}2} u = 2gammabeta e^{beta|u|^2}u$ on $d$-dimensional compact Riemannian manifolds $mathcal{M}
In this paper we consider the initial value {problem $partial_{t} u- Delta u=f(u),$ $u(0)=u_0in exp,L^p(mathbb{R}^N),$} where $p>1$ and $f : mathbb{R}tomathbb{R}$ having an exponential growth at infinity with $f(0)=0.$ Under smallness condition on th
We present a numerical study of solutions to the $2d$ focusing nonlinear Schrodinger equation in the exterior of a smooth, compact, strictly convex obstacle, with Dirichlet boundary conditions with cubic and quintic powers of nonlinearity. We study t
We consider the nonlinear Schrodinger equation [ u_t = i Delta u + | u |^alpha u quad mbox{on ${mathbb R}^N $, $alpha>0$,} ] for $H^1$-subcritical or critical nonlinearities: $(N-2) alpha le 4$. Under the additional technical assumptions $alphageq 2$
In this paper we prove local well-posedness in Orlicz spaces for the biharmonic heat equation $partial_{t} u+ Delta^2 u=f(u),;t>0,;xinR^N,$ with $f(u)sim mbox{e}^{u^2}$ for large $u.$ Under smallness condition on the initial data and for exponential