Abstract: In this article, the authors consider the collapse solutions of Cauchy problem
for the nonlinear Schrödinger equation i Ψ _t + 1/ 2 △ Ψ- 1 /2 ω²|x|² ψ+|ψ|²ψ = 0, x ∈ R², which models the Bose-Einstein condensate with attractive interactions. The authors establish the lower bound of collapse rate as t → T. Furthermore, the L²-concentration property of the radially symmetric collapse solutions is obtained.

Key words: Nonlinear Schrö, dinger equation, attractive Bose-Einstein condensates, col-
lapse rate, L²-concentration