Orbital stability of bound states of semiclassical nonlinear schrödinger equations with critical nonlinearity
Journal
SIAM Journal on Mathematical Analysis
Journal Volume
40
Journal Issue
1
Pages
365-381
Date Issued
2008
Author(s)
Wei, J.
Abstract
We consider the orbital stability of single-spike bound states of semiclassical nonlinear Schr?dinger equations with critical nonlinearity and a trap potential. Due to the effect of the trap potential, we derive the asymptotic expansion formulas and obtain the necessary conditions for orbital stability and instability of single-spike bound states. Our argument is applied to two-component systems of nonlinear Schr?dinger equations with a common trap potential, cubic nonlinearity in two spatial dimensions. The orbital stability of bound states with spikes of these systems is investigated. Our results show the existence of stable spikes in two-dimensional Bose�VEinstein condensates.
SDGs
Type
journal article