Analysis Seminar

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On multi-dimensional compact solitary patterns

Speaker: Philip Rosenau, Tel Aviv University

Location: Warren Weaver Hall 1302

Date: Thursday, October 19, 2017, 11 a.m.

Synopsis:

As though to compensate for the rarity of multidimensional integrable systems in
higher dimensions, spatial extensions of many of the well-known nonlinear dispersive
equations on the line, exhibit a remarkably rich variety of solitary patterns unavailable
in 1-D. Our work systematizes this observation with a special attention paid to
compactons - solitary waves with compact support - where this effect is found to be
far more pronounced and begets a zoo of multi-dimensional compact solitary patterns.

One manifestation of this phenomenon is found in the sublinear NLS and Complex
Klein-Gordon where the compactons inducing mechanism coupled with azimuthal
spinning may expel the compact vortices from the origin to form a finite or countable
number of genuine ring-vortices. Such rings are an exclusive feature of compacton
supporting systems.