Displaying similar documents to “Dunkl-Schrödinger Equations with and without Quadratic Potentials”

Weak Asymptotics for Schrödinger Evolution

S. A. Denisov (2010)

Mathematical Modelling of Natural Phenomena

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In this short note, we apply the technique developed in [Math. Model. Nat. Phenom., 5 (2010), No. 4, 122-149] to study the long-time evolution for Schrödinger equation with slowly decaying potential.

Nonlinear Schrödinger equation on four-dimensional compact manifolds

Patrick Gérard, Vittoria Pierfelice (2010)

Bulletin de la Société Mathématique de France

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We prove two new results about the Cauchy problem in the energy space for nonlinear Schrödinger equations on four-dimensional compact manifolds. The first one concerns global well-posedness for Hartree-type nonlinearities and includes approximations of cubic NLS on the sphere as a particular case. The second one provides, in the case of zonal data on the sphere, local well-posedness for quadratic nonlinearities as well as a necessary and sufficient condition of global well-posedness...

Dispersion Phenomena in Dunkl-Schrödinger Equation and Applications

Mejjaoli, H. (2009)

Serdica Mathematical Journal

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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.

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

Changxing Miao, Youbin Zhu (2006)

Annales Polonici Mathematici

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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...