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Philip Rosenau
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Tel Aviv University
On multi-dimensional compact solitary patterns
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.