The low energy scattering for nonlinear Schrödinger equation

2021 ◽  
Author(s):  
Conghui Fang ◽  
Zheng Han
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Low Energy ◽  
Nonlinear Schrödinger ◽  
Energy Scattering

scholarly journals NONCOMMUTATIVE SPACE AND THE LOW-ENERGY PHYSICS OF QUASICRYSTALS

2008 ◽  
Vol 23 (13) ◽  
pp. 2037-2045 ◽  
Author(s):  
L. MONREAL ◽  
P. FERNÁNDEZ DE CÓRDOBA ◽  
A. FERRANDO ◽  
J. M. ISIDRO
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Low Energy ◽  
Noncommutative Space ◽  
Nonlinear Schrödinger ◽  
Quasiperiodic Potential ◽  
Space Noncommutativity ◽  
Energy Physics

We prove that the effective low-energy, nonlinear Schrödinger equation for a particle in the presence of a quasiperiodic potential is the potential-free, nonlinear Schrödinger equation on noncommutative space. Thus quasiperiodicity of the potential can be traded for space noncommutativity when describing the envelope wave of the initial quasiperiodic wave.

scholarly journals Energy scattering for a class of inhomogeneous nonlinear Schrödinger equation in two dimensions

2021 ◽  
Vol 18 (01) ◽  
pp. 1-28
Author(s):  
Van Duong Dinh
Keyword(s):  
Initial Data ◽  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Two Dimensions ◽  
Nonlinear Schrödinger ◽  
Energy Scattering ◽  
The One ◽  
Inhomogeneous Nonlinear Schrödinger Equation

We consider a class of [Formula: see text]-supercritical inhomogeneous nonlinear Schrödinger equations in two dimensions [Formula: see text] where [Formula: see text] and [Formula: see text]. Using a new approach of Arora et al. [Scattering below the ground state for the 2D radial nonlinear Schrödinger equation, Proc. Amer. Math. Soc. 148 (2020) 1653–1663], we show the energy scattering for the equation with radially symmetric initial data. In the focusing case, our result extends the one of Farah and Guzmán [Scattering for the radial focusing INLS equation in higher dimensions, Bull. Braz. Math. Soc. (N.S.) 51 (2020) 449–512] to the whole range of [Formula: see text] where the local well-posedness is available. In the defocusing case, our result extends the one in [V. D. Dinh, Energy scattering for a class of the defocusing inhomogeneous nonlinear Schrödinger equation, J. Evol. Equ. 19(2) (2019) 411–434], where the energy scattering for non-radial initial data was established in dimensions [Formula: see text].

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