Analysis Seminar

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Multi-Dimensional Compact Patterns

Speaker: Philip Rosneau, Tel-Aviv University

Location: Warren Weaver Hall 1302

Date: Thursday, May 22, 2014, 11 a.m.

Synopsis:

Solitons, kinks or breathers, are manifestations of weakly nonlinear excitations in, say, anharmonic mass-particle chains. In a strongly anharmonic chains, the tails of the emerging patterns rather than exponentially, decay at a doubly-exponential rate and in the continuum limit collapse into a singular surface with the resulting waves becoming strictly compact, hence their name: compactons. Using the Z-K, the Sub-linear Complex Klein-Gordon and the Sub-linear NLS equations as examples, we shall show how typical multidimensional compactons emergence and interact. In general, for compact- and hence non-analytical, structures to emerge, the underlying system has to admit a local loss of uniqueness due to, for instance, a degeneracy of the highest order operator or other, singularity inducing, mechanisms.