PMID: 19113773Dec 31, 2008Paper

Compactification of nonlinear patterns and waves

Physical Review Letters
Philip Rosenau, Eugene Kashdan

Abstract

We present a nonlinear mechanism(s) which may be an alternative to a missing wave speed: it induces patterns with a compact support and sharp fronts which propagate with a finite speed. Though such mechanism may emerge in a variety of physical contexts, its mathematical characterization is universal, very simple, and given via a sublinear substrate (site) force. Its utility is shown studying a Klein-Gordon -u(tt) + [phi/(u(x)]x = P'(u) equation, where phi'(sigma) = sigma + beta sigma3 and endowed with a subquadratic site potential P(u) approximately /1-u2/(alpha+1), 0 < or = alpha < 1, and the Schrödinger iZt + inverted delta2 Z = G(/Z/)Z equation in a plane with G(A) = gammaA(-delta) - sigmaA2, 0 < delta < or = 1.

References

Feb 1, 1993·Physical Review Letters·P Rosenau, J M Hyman
Mar 24, 2005·Physical Review Letters·P Rosenau, S Schochet
May 21, 2005·Physical Review Letters·Philip Rosenau, Arkady Pikovsky
Mar 16, 2007·Physical Review Letters·Philip RosenauMartin Staley
Feb 1, 2008·Physical Review Letters·Philip Rosenau

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Citations

Nov 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Fabien Kenmogne, David Yemélé
Feb 18, 2017·Physical Review. E·Chancelor Pokam NguewaweDavid Yemélé
Jul 30, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Andres CardenasAvadh Saxena
Jan 15, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Bogdan MihailaAvadh Saxena
Apr 7, 2010·Physical Review Letters·Philip Rosenau, Eugene Kashdan
Sep 28, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Bogdan MihailaAvadh Saxena

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