Collapses of Wavefunctions in Multi-Dimensional Coupled Nonlinear Schrödinger Equations under Harmonic Potentials

抄録

By generalizing the Zakharov's theory for collapses of Langmuir waves, we investigate the instabilities of wavefunctions in the D-dimensionalN-component coupled nonlinear Schrödinger equations under harmonicpotentials. We show that all wavefunctions surely collapse in a finite time, when the total energy is negative.For a special case that D=2 and all coefficients of harmonicpotential terms are equal, we predict that the collapse can occur even when some fields interact repulsively.