A note on coupled focusing nonlinear Schrodinger equations

Abstract

Some focusing coupled Schrödinger equations are investigated. First, existence of ground state is obtained. Second, global and non global existence of solutions are discussed via potential-well method. Finally, strong instability of standing waves is established.

On coupled nonlinear Schrodinger equations with harmonic potential

“…Readers are referred, for instance, to [12,29] for the derivation and applications of this system. Well-posedness issues in the energy space of (CNLS) p were recently investigated by many authors [23,24,17]. A solution u := (u 1 , ..., u m ) to (1.1) formally satisfies respectively conservation of the mass and the energy M(u j ) := If µ = 1, the energy is always positive and we say that the problem (1.1) is defocusing, otherwise it is focusing.…”