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

Journal Article · Tue Feb 01 04:00:00 EST 2000 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.61.2006· OSTI ID:20215475

Kevrekidis, P G ^[1]; Rasmussen, K Oe ^[1]; Bishop, A R ^[1]

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1. Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)

We develop a methodology for the construction of two-dimensional discrete breather excitations. Application to the discrete nonlinear Schroedinger 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. (c) 2000 The American Physical Society.

• OSTI ID: 20215475
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 2 Vol. 61; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BIFURCATION
EXCITATION
PHONONS
SCHROEDINGER EQUATION
STABILITY
THEORETICAL DATA
TRIPLE POINT