Soliton dynamics of NLS with singular potentials

TL;DR

This paper studies how solitons behave in a nonlinear Schrödinger equation with singular external potentials, especially in the semi-relativistic limit, revealing insights into their dynamics in higher dimensions.

Contribution

It provides new analysis on soliton dynamics for NLS with singular potentials in the semi-relativistic regime, extending previous understanding to more complex external influences.

Findings

Validation of soliton dynamics in the semi-relativistic limit

Analysis of soliton behavior with singular potentials in higher dimensions

Extension of soliton theory to more general external fields

Abstract

We investigate the validity of a soliton dynamics behavior in the semi-relativistic limit for the nonlinear Schr\"odinger equation in $\R^{N}, N\ge 3$, in presence of a singular external potential.