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Collapse in the nonlinear Schrödinger equation of critical dimension {σ = 1, D = 2}

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Ovchinnikov,  Y. N.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Ovchinnikov, Y. N., & Sigal, I. M. (2002). Collapse in the nonlinear Schrödinger equation of critical dimension {σ = 1, D = 2}. JETP Letters, 75(7), 357-361. Retrieved from http://ojps.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JTPLA2000075000007000357000001&idtype=cvips&gifs=Yes.


Cite as: http://hdl.handle.net/11858/00-001M-0000-002B-38B9-9
Abstract
Collapsing solutions to the nonlinear Schrodinger equation of critical dimension {sigma = 1, D = 2} are analyzed in the adiabatic approximation. A three-parameter set of solutions is obtained for the scale factor lambda(t). It is shown that the Talanov solution lies on the separatrix between the regions of collapse and convenient expansion. A comparison with numerical solutions indicates that weakly collapsing solutions provide a good initial approximation to the collapse problem. (C) 2002 MAIK "Nauka / Interperiodica".