Soliton dynamics for a general class of Schr\"odinger equations

TL;DR

This paper investigates the behavior of solitons in a broad class of nonlinear focusing Schrödinger equations with variable external potentials, analyzing their dynamics starting from ground state initial conditions.

Contribution

It introduces a general framework for studying soliton dynamics in Schrödinger equations with both local and nonlocal potentials, extending previous models.

Findings

Characterization of soliton stability under variable potentials

Analysis of soliton trajectories influenced by external potentials

Conditions for soliton persistence and scattering

Abstract

The soliton dynamics for a general class of nonlinear focusing Schr\"odinger problems in presence of non-constant external (local and nonlocal) potentials is studied by taking as initial datum the ground state solution of an associated autonomous elliptic equation.