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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Hydrodynamic approach to constructing solutions of the nonlinear Schrödinger equation in the critical case


Author: O. S. Rozanova
Journal: Proc. Amer. Math. Soc. 133 (2005), 2347-2358
MSC (2000): Primary 35Q55; Secondary 35K55
Published electronically: March 22, 2005
MathSciNet review: 2138877
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Abstract: Proceeding from the hydrodynamic approach, we construct exact solutions to the nonlinear Schrödinger equation with special properties. The solutions describe collapse, in finite time, and scattering, over infinite time, of wave packets. They generalize known blow-up solutions based on the ``ground state''.


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Additional Information

O. S. Rozanova
Affiliation: Department of Differential Equations, Mathematics and Mechanics Faculty, Moscow State University, GSP-2 Vorobiovy Gory, Moscow 119992, Russia
Email: rozanova@mech.math.msu.su

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07920-7
PII: S 0002-9939(05)07920-7
Keywords: Nonlinear Schr\"odinger equation, hydrodynamic approach, integral functionals, exact solutions, blow-up solutions
Received by editor(s): December 10, 2003
Published electronically: March 22, 2005
Communicated by: Mark J. Ablowitz
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.