Strong Magnetic Field Limit in a Nonlinear Iwatsuka-Type Model

TL;DR

This paper investigates the behavior of a nonlinear Schrödinger equation with a magnetic field that varies only along one spatial dimension, revealing an effective nonlocal model and confinement effects in the strong magnetic field limit.

Contribution

It introduces a high-frequency averaging approach to derive a nonlocal nonlinear model from a nonlinear Iwatsuka-type Schrödinger equation in the strong magnetic field regime.

Findings

Effective nonlocal nonlinear model derived

Inhomogeneous nonlinearities are confined along the y-axis

The original equation becomes non-dispersive in the limit

Abstract

We study the strong magnetic field limit for a nonlinear Iwatsuka-type model, i.e. a nonlinear Schr\"odinger equation in two spatial dimensions with a magnetic vector potential that only depends on the $x$-coordinate. Using a high-frequency averaging technique, we show that this equation can be effectively described by a nonlocal nonlinear model, which is no longer dispersive. We also prove that, in this asymptotic regime, inhomogeneous nonlinearities are confined along the $y$-axis.