Soliton dynamics for fractional Schrödinger equations

Abstract

We investigate the soliton dynamics for the fractional nonlinear Schrödinger equation by a suitable modulational inequality. In the semiclassical limit, the solution concentrates along a trajectory determined by a Newtonian equation depending of the fractional diffusion parameter.

Keywords:

• soliton dynamics
• fractional Schrödinger equation
• ground states

AMS Subject Classifications:

• 35Q51
• 35Q40
• 35Q41

Acknowledgements

S. Secchi is supported by 2009 PRIN Critical Point Theory and Perturbative Methods for Nonlinear Differential Equations and by 2012 FIRB Dispersive equations and Fourier analysis, while M. Squassina is supported by 2009 PRIN Variational and Topological Methods in the Study of Nonlinear Phenomena.