Hydrodynamic approach to constructing solutions of the nonlinear Schrödinger equation in the critical case |
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| Authors: | O S Rozanova |
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| Institution: | Department of Differential Equations, Mathematics and Mechanics Faculty, Moscow State University, GSP-2 Vorobiovy Gory, Moscow 119992, Russia |
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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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| Keywords: | Nonlinear Schr\"odinger equation hydrodynamic approach integral functionals exact solutions blow-up solutions |
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