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arXiv · 1307.5523

Orbital stability of standing waves of a class of fractional Schrodinger equations with a general Hartree-type integrand

Y. Cho·M. M. Fall·H. Hajaiej·P. A. Markowich·S. Trabelsi
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Abstract

This article is concerned with the mathematical analysis of a class of a nonlinear fractional Schrodinger equations with a general Hartree-type integrand. We prove existence and uniqueness of global-in-time solutions to the associated Cauchy problem. Under suitable assumptions, we also prove the existence of standing waves using the method of concentration-compactness by studying the associated constrained minimization problem. Finally we show the orbital stability of standing waves which are the minimizers of the associate variational problem.

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Y. Cho, M. M. Fall, H. Hajaiej, P. A. Markowich, S. Trabelsi. 2013-07-21. Orbital stability of standing waves of a class of fractional Schrodinger equations with a general Hartree-type integrand. https://arxiv.org/abs/1307.5523

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