ﻻ يوجد ملخص باللغة العربية
We study the nonlinear Schrodinger equation with initial data in $mathcal{Z}^s_p(mathbb{R}^d)=dot{H}^s(mathbb{R}^d)cap L^p(mathbb{R}^d)$, where $0<s<min{d/2,1}$ and $2<p<2d/(d-2s)$. After showing that the linear Schrodinger group is well-defined in this space, we prove local well-posedness in the whole range of parameters $s$ and $p$. The precise properties of the solution depend on the relation between the power of the nonlinearity and the integrability $p$. Finally, we present a global existence result for the defocusing cubic equation in dimension three for initial data with infinite mass and energy, using a variant of the Fourier truncation method.
We consider nonlinear Schr{o}dinger equations in Fourier-Lebesgue and modulation spaces involving negative regularity. The equations are posed on the whole space, and involve a smooth power nonlinearity. We prove two types of norm inflation results.
In this paper we prove some multi-linear Strichartz estimates for solutions to the linear Schrodinger equations on torus $T^n$. Then we apply it to get some local well-posed results for nonlinear Schrodinger equation in critical $H^{s}(T^n)$ spaces.
In this paper, we analyse a new exponential-type integrator for the nonlinear cubic Schrodinger equation on the $d$ dimensional torus $mathbb T^d$. The scheme has recently also been derived in a wider context of decorated trees in [Y. Bruned and K. S
For the solution of the cubic nonlinear Schrodinger equation in one space dimension, we propose and analyse a fully discrete low-regularity integrator. The scheme is explicit and can easily be implemented using the fast Fourier transform with a compl
The initial-boundary value problem (IBVP) for the nonlinear Schrodinger (NLS) equation on the half-plane with nonzero boundary data is studied by advancing a novel approach recently developed for the well-posedness of the cubic NLS on the half-line,