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Zbl 1166.35377
Zhang, Jian; Li, Xiaoguang; Wu, Yonghong
Remarks on the blow-up rate for critical nonlinear Schrödinger equation with harmonic potential.
(English)
[J] Appl. Math. Comput. 208, No. 2, 389-396 (2009). ISSN 0096-3003

Summary: We consider the blow-up solutions of the Cauchy problem for the critical nonlinear Schrödinger equation with a harmonic potential, which models the attractive Bose-Einstein condensate. We establish the sharp lower and upper bounds of blow-up rate as $t\rightarrow T$ (blow-up time), which improve the result of {\it Q. Liu, Y. Zhou} and {\it J. Zhang} [Appl. Math. Comput. 172, No.~2, 1121--1132 (2006; Zbl 1091.35092)].
MSC 2000:
*35Q55 NLS-like (nonlinear Schroedinger) equations
35B40 Asymptotic behavior of solutions of PDE
35B45 A priori estimates
81V80 Appl. of quantum theory to quantum optics

Keywords: blow-up rate; nonlinear Schrödinger equation; harmonic potential; attractive Bose-Einstein condensates

Citations: Zbl 1091.35092

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