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Two-dimensional discrete breathers: Construction, stability, and bifurcations

P. G. Kevrekidis1,2, K. Ø. Rasmussen1, and A. R. Bishop1

  • 1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
  • 2Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, New Jersey 08854-8019

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Phys. Rev. E 61, 2006 – Published 1 February, 2000

DOI: https://doi.org/10.1103/PhysRevE.61.2006

Abstract

We develop a methodology for the construction of two-dimensional discrete breather excitations. Application to the discrete nonlinear Schrödinger equation on a square lattice reveals three different types of breathers. Considering an elementary plaquette, the most unstable mode is centered on the plaquette, the most stable mode is centered on its vertices, while the intermediate (but also unstable) mode is centered at the middle of one of the edges. Below the turning points of each branch in a frequency-power phase diagram, the construction methodology fails and a continuation method is used to obtain the unstable branches of the solutions until a triple point is reached. At this triple point, the branches meet and subsequently bifurcate into the final state of an extended phonon mode.

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Phys. Rev. E 61, 2006– Published 1 February, 2000
  • Received 1 September 1999

© 2000 American Physical Society

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