Soliton dynamics for fractional Schrodinger equations

TL;DR

This paper studies the behavior of solitons in fractional nonlinear Schrödinger equations, showing how solutions concentrate along trajectories governed by a Newtonian equation influenced by fractional diffusion.

Contribution

It introduces a modulational inequality approach to analyze soliton dynamics in fractional Schrödinger equations, linking solution concentration to fractional diffusion parameters.

Findings

Solutions concentrate along Newtonian trajectories

Fractional diffusion influences soliton paths

Semiclassical limit behavior characterized

Abstract

We investigate the soliton dynamics for the fractional nonlinear Schrodinger 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.