Runzhang Xu, Chuang Xu
Abstract:
This article studies a nonlinear Schodinger equation with harmonic
potential by constructing different cross-constrained problems. By
comparing the different cross-constrained problems, we derive
different sharp criterion and different invariant manifolds that
separate the global solutions and blowup solutions. Moreover, we
conclude that some manifolds are empty due to the essence of the
cross-constrained problems. Besides, we compare the three
cross-constrained problems and the three depths of the potential
wells. In this way, we explain the gaps in [J. Shu and J.
Zhang, Nonlinear Shrodinger equation with harmonic
potential, Journal of Mathematical Physics, 47, 063503 (2006)],
which was pointed out in [R. Xu and Y. Liu, Remarks on nonlinear
Schrodinger equation with harmonic potential, Journal of
Mathematical Physics, 49, 043512 (2008)].
Submitted August 3, 2012. Published November 27, 2012.
Math Subject Classifications: 78A60, 35Q55.
Key Words: Cross-constrained problem; blow up; global existence;
invariant manifold; harmonic potential.
Show me the PDF file (516 KB), TEX file, and other files for this article.
 |
Runzhang Xu Department of Applied Mathematics Harbin Engineering University, 150001, China email: xurunzh@yahoo.com.cn |
|---|---|
 |
Chuang Xu Department of Mathematiccal and Statistical Sciences University of Alberta, Edmonton T6G 2G1, Alberta, Canada Department of Mathematics Harbin Institute of Technology, 150001, China email: xuchuang6305@163.com |
Return to the EJDE web page