ﻻ يوجد ملخص باللغة العربية
In this paper, we show the scattering of the solution for the focusing inhomogenous nonlinear Schrodinger equation with a potential begin{align*} ipartial_t u+Delta u- Vu=-|x|^{-b}|u|^{p-1}u end{align*} in the energy space $H^1(mathbb R^3)$. We prove a scattering criterion, and then we use it together with Morawetz estimate to show the scattering theory.
In this paper we consider the inhomogeneous nonlinear Schrodinger equation $ipartial_t u +Delta u=K(x)|u|^alpha u,, u(0)=u_0in H^s({mathbb R}^N),, s=0,,1,$ $Ngeq 1,$ $|K(x)|+|x|^s| abla^sK(x)|lesssim |x|^{-b},$ $0<b<min(2,N-2s),$ $0<alpha<{(4-2b)/(N-
In this paper, we study the long-time behavior of global solutions to the Schrodinger-Choquard equation $$ipartial_tu+Delta u=-(I_alphaast|cdot|^b|u|^{p})|cdot|^b|u|^{p-2}u.$$ Inspired by Murphy, who gave a simple proof of scattering for the non-ra
We study the instability of standing-wave solutions $e^{iomega t}phi_{omega}(x)$ to the inhomogeneous nonlinear Schr{o}dinger equation $$iphi_t=-trianglephi+|x|^2phi-|x|^b|phi|^{p-1}phi, qquad inmathbb{R}^N, $$ where $ b > 0 $ and $ phi_{omega} $ is
We prove sharp $L^infty$ decay and modified scattering for a one-dimensional dispersion-managed cubic nonlinear Schrodinger equation with small initial data chosen from a weighted Sobolev space. Specifically, we work with an averaged version of the d
We consider the $1d$ cubic nonlinear Schrodinger equation with a large external potential $V$ with no bound states. We prove global regularity and quantitative bounds for small solutions under mild assumptions on $V$. In particular, we do not require