ﻻ يوجد ملخص باللغة العربية
In this paper, we give a simple proof of scattering result for the Schrodinger equation with combined term $ipa_tu+Delta u=|u|^2u-|u|^4u$ in dimension three, that avoids the concentrate compactness method. The main new ingredient is to extend the scattering criterion to energy-critical.
We adapt the argument of Dodson-Murphy to give a simple proof of scattering below the ground state for the intercritical inhomogeneous nonlinear Schrodinger equation. The decaying factor in the nonlinearity obviates the need for a radial assumption.
In this paper, we study the scattering theory for the cubic inhomogeneous Schrodinger equations with inverse square potential $iu_t+Delta u-frac{a}{|x|^2}u=lambda |x|^{-b}|u|^2u$ with $a>-frac14$ and $0<b<1$ in dimension three. In the defocusing case
We extend the result of Farah and Guzman on scattering for the $3d$ cubic inhomogeneous NLS to the non-radial setting. The key new ingredient is a construction of scattering solutions corresponding to initial data living far from the origin.
We prove scattering below the ground state threshold for an energy-critical inhomogeneous nonlinear Schrodinger equation in three space dimensions. In particular, we extend results of Cho, Hong, and Lee from the radial to the non-radial setting.
In this paper, we study the long time behavior of the solution of nonlinear Schrodinger equation with a singular potential. We prove scattering below the ground state for the radial NLS with inverse-square potential in dimension two $$iu_t+Delta u-