Displaying similar documents to “Weak Asymptotics for Schrödinger Evolution”

Dispersion Phenomena in Dunkl-Schrödinger Equation and Applications

Mejjaoli, H. (2009)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: 35Q55,42B10. In this paper, we study the Schrödinger equation associated with the Dunkl operators, we study the dispersive phenomena and we prove the Strichartz estimates for this equation. Some applications are discussed.

Schrödinger maps

Daniel Tataru (2012)

Journées Équations aux dérivées partielles

Similarity:

The Schrödinger map equation is a geometric Schrödinger model, closely associated to the harmonic heat flow and to the wave map equation. The aim of these notes is to describe recent and ongoing work on this model, as well as a number of related open problems.

Hardy's uncertainty principle, convexity and Schrödinger evolutions

Luis Escauriaza, Carlos E. Kenig, G. Ponce, Luis Vega (2008)

Journal of the European Mathematical Society

Similarity:

We prove the logarithmic convexity of certain quantities, which measure the quadratic exponential decay at infinity and within two characteristic hyperplanes of solutions of Schrödinger evolutions. As a consequence we obtain some uniqueness results that generalize (a weak form of) Hardy’s version of the uncertainty principle. We also obtain corresponding results for heat evolutions.

The Cauchy problem for the coupled Klein-Gordon-Schrödinger system

Changxing Miao, Youbin Zhu (2006)

Annales Polonici Mathematici

Similarity:

We consider the Cauchy problem for a generalized Klein-Gordon-Schrödinger system with Yukawa coupling. We prove the existence of global weak solutions by the compactness method and, through a special choice of the admissible pairs to match two types of equations, we prove the uniqueness of those solutions by an approach similar to the method presented by J. Ginibre and G. Velo for the pure Klein-Gordon equation or pure Schrödinger equation. Though it is very simple in form, the method...

Stationary solutions of semilinear Schrödinger equations with trapping potentials in supercritical dimensions

Filip Ficek (2023)

Archivum Mathematicum

Similarity:

Nonlinear Schrödinger equations are usually investigated with the use of the variational methods that are limited to energy-subcritical dimensions. Here we present the approach based on the shooting method that can give the proof of existence of the ground states in critical and supercritical cases. We formulate the assumptions on the system that are sufficient for this method to work. As examples, we consider Schrödinger-Newton and Gross-Pitaevskii equations with harmonic potentials. ...

Dunkl-Schrödinger Equations with and without Quadratic Potentials

Mejjaoli, Hatem (2011)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: Primary 42A38. Secondary 42B10. The purpose of this paper is to study the dispersive properties of the solutions of the Dunkl-Schrödinger equation and their perturbations with potential. Furthermore, we consider a few applications of these results to the corresponding nonlinear Cauchy problems.

Resonances of two-dimensional Schrödinger operators with strong magnetic fields

Tuan Duong, Anh (2012)

Serdica Mathematical Journal

Similarity:

2010 Mathematics Subject Classification: 81Q20 (35P25, 81V10). The purpose of this paper is to study the Schrödinger operator P(B,w) = (Dx-By^2+Dy^2+w^2x^2+V(x,y),(x,y) О R^2, with the magnetic field B large enough and the constant w № 0 is fixed and proportional to the strength of the electric field. Under certain assumptions on the potential V, we prove the existence of resonances near Landau levels as B®Ґ. Moreover, we show that the width of resonances is of size O(B^-Ґ). ...