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nlin.PS2013★ 11 cited
Logarithmic scaling of the collapse in the critical Keller-Segel equation
Sergey A. Dyachenko, Pavel M. Lushnikov, Natalia Vladimirova
A reduced Keller-Segel equation (RKSE) is a parabolic-elliptic system of partial differential equations which describes bacterial aggregation and the collapse of a self-gravitating…
nlin.PS2012★ 20 cited
Beyond leading order logarithmic scaling in the catastrophic self-focusing (collapse) of a laser beam in Kerr media
Pavel M. Lushnikov, Sergey A. Dyachenko, Natalia Vladimirova
We study the catastrophic stationary self-focusing (collapse) of laser beam in nonlinear Kerr media. The width of a self-similar solutions near collapse distance obeys $(z_…