Concentrations for nonlinear Schrodinger equation with magnetic potentials and constant electric potentials

TL;DR

This paper investigates how magnetic fields influence the concentration points of solutions to nonlinear Schrödinger equations with constant electric potentials, revealing a new role of magnetic fields in such scenarios.

Contribution

It introduces the novel finding that magnetic fields significantly affect concentration locations when electric potentials are constant, unlike previous cases with variable electric potentials.

Findings

Magnetic fields influence concentration points.

Electric potential constancy alters concentration behavior.

New insights into magnetic effects in Schrödinger equations.

Abstract

This paper studies the concentration phenomena to nonlinear Schrodinger equations with magnetic potentials and constant electric potentials. We find that the magnetic field plays an important role in the location of concentrations if the electric potential is constant. This is a completely new result compared with the case of non-constant electric potentials.