Strong Magnetic Field Limit in a Nonlinear Iwatsuka-Type Model

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.