MODIFIED SCATTERING FOR THE CUBIC SCHRÖDINGER EQUATION ON PRODUCT SPACES AND APPLICATIONS
نویسندگان
چکیده
منابع مشابه
Nonlinear Schrödinger Equation on Real Hyperbolic Spaces
We consider the Schrödinger equation with no radial assumption on real hyperbolic spaces. We obtain sharp dispersive and Strichartz estimates for a large family of admissible pairs. As a first consequence, we obtain strong wellposedness results for NLS. Specifically, for small intial data, we prove L 2 and H 1 global wellposedness for any subcritical nonlinearity (in contrast with the flat case...
متن کاملṕ Estimates for the Schrödinger Equation on the Line and Inverse Scattering for the Nonlinear Schrödinger Equation with a Potential ∗
In this paper I prove a L − L estimate for the solutions of the one–dimensional Schrödinger equation with a potential in Lγ where in the generic case γ > 3/2 and in the exceptional case (i.e. when there is a half–bound state of zero energy) γ > 5/2. I use this estimate to construct the scattering operator for the nonlinear Schrödinger equation with a potential. I prove moreover, that the low–en...
متن کاملExistence, stability, and scattering of bright vortices in the cubic-quintic nonlinear Schrödinger equation
We revisit the topic of the existence and azimuthal modulational stability of solitary vortices (alias vortex solitons) in the twodimensional (2D) cubic–quintic nonlinear Schrödinger equation. We develop a semi-analytical approach, assuming that the vortex soliton is relatively narrow, which allows one to effectively split the full 2D equation into radial and azimuthal 1D equations. A variation...
متن کاملGeneralized hyperstability of the cubic functional equation in ultrametric spaces
In this paper, we present the generalized hyperstability results of cubic functional equation in ultrametric Banach spaces using the fixed point method.
متن کاملLong Range Scattering for the Cubic Dirac Equation on R
We show that the cubic Dirac equation, also known as the Thirring model, scatters at infinity to a linear solution modulo a phase correction.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Forum of Mathematics, Pi
سال: 2015
ISSN: 2050-5086
DOI: 10.1017/fmp.2015.5