A note on coupled nonlinear Schrödinger equations

Abstract

We investigate the initial value problem for some coupled nonlinear Schrödinger equations in two space dimensions with exponential growth. We prove global well-posedness and scattering in the defocusing case. In the focusing sign, existence of non-global solution is discussed via the potential-well theory.

A note on coupled focusing nonlinear Schrodinger equations

“…In two space dimensions, similar results about global well-posedness and scattering of the Schrödinger equation with exponential nonlinearity exist [20,22,23,21].…”

Coupled nonlinear Schrödinger equations with harmonic potential

“…Intensive work has been done in the last few years about coupled Schrödinger systems [18,19,24,29]. These works have been mainly on 2-systems or with small couplings.…”

“…Readers are referred, for instance, to [14,30] for the derivation and applications of this system. Well-posedness issues in the energy space of (CNLS) p were recently investigated by many authors [19,25,26]. …”

On coupled nonlinear Schrodinger equations with harmonic potential

“…Intensive work has been done in the last few years about coupled Schrödinger systems [17,28,16,22]. These works have been mainly on 2-systems or with small couplings.…”