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We study the strong magnetic field limit for a nonlinear Iwatsuka-type model, i.e. a nonlinear Schrödinger 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. [ABSTRACT FROM AUTHOR]

Abstract: We consider a cubic nonlinear Schrödinger equation with periodic potential. In a semiclassical scaling the nonlinear interaction of modulated pulses concentrated in one or several Bloch bands is studied. The notion of closed mode systems is introduced which allows for the rigorous derivation of a finite system of amplitude equations describing the macroscopic interaction of these pulses. [Copyright &y& Elsevier]