Proceedings of the American Mathematical Society

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

Author(s): O. S. Rozanova
Journal: Proc. Amer. Math. Soc. 133 (2005), 2347-2358.
MSC (2000): Primary 35Q55; Secondary 35K55
Posted: March 22, 2005
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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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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 35Q55, 35K55

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: 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
Posted: March 22, 2005
Communicated by: Mark J. Ablowitz
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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