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q-Breathers in Finite Two-and Three-Dimensional Nonlinear Acoustic Lattices M. V. Ivanchenko,1

Summary: q-Breathers in Finite Two- and Three-Dimensional Nonlinear Acoustic Lattices
M. V. Ivanchenko,1
O. I. Kanakov,1
K. G. Mishagin,1
and S. Flach2
Department of Radiophysics, Nizhny Novgorod University, Gagarin Avenue 23, 603950 Nizhny Novgorod, Russia
Max-Planck-Institut fu¨r Physik komplexer Systeme, No¨thnitzer Strasse 38, D-01187 Dresden, Germany
(Received 28 April 2006; published 14 July 2006)
In their celebrated experiment, Fermi, Pasta, and Ulam (FPU) [Los Alamos Report No. LA-1940, 1955]
observed that in simple one-dimensional nonlinear atomic chains the energy must not always be equally
shared among the modes. Recently, it was shown that exact and stable time-periodic orbits, coined
q-breathers (QBs), localize the mode energy in normal mode space in an exponential way, and account for
many aspects of the FPU problem. Here we take the problem into more physically important cases of two-
and three-dimensional acoustic lattices to find existence and principally different features of QBs. By use
of perturbation theory and numerical calculations we obtain that the localization and stability of QBs are
enhanced with increasing system size in higher lattice dimensions opposite to their one-dimensional
DOI: 10.1103/PhysRevLett.97.025505 PACS numbers: 63.20.Pw, 05.45.ÿa, 63.20.Ry


Source: Aickelin, Uwe - School of Computer Science, University of Nottingham
Flach, Sergej - Max-Planck-Institut für Physik komplexer Systeme


Collections: Computer Technologies and Information Sciences; Physics