期刊
PHYSICA D-NONLINEAR PHENOMENA
卷 244, 期 1, 页码 1-24出版社
ELSEVIER
DOI: 10.1016/j.physd.2012.10.008
关键词
Nonlinear lattices; Discrete Hamiltonian systems; Escape dynamics; Collapse; Modulation instability; Breathers
资金
- MICINN [FIS2008-04848]
- Special Account for Research Grants of the University of Athens
- US National Science Foundation [NSF-DMS-0806762, NSF-CMMI-1000337]
- US Air Force [FA9550-12-1-0332]
- Alexander von Humboldt Foundation
- Alexander S. Onassis Public Benefit Foundation [RZG 003/2010-2011]
- Binational Science Foundation [2010239]
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [1000337] Funding Source: National Science Foundation
We study deterministic escape dynamics of the discrete Klein-Gordon model with a repulsive quartic on-site potential. Using a combination of analytical techniques, based on differential and algebraic inequalities and selected numerical illustrations, we first derive conditions for collapse of an initially excited single-site unit, for both the Hamiltonian and the linearly damped versions of the system and showcase different potential fates of the single-site excitation, such as the possibility to be pulled back from outside the well or to drive over the barrier some of its neighbors. Next, we study the evolution of a uniform (small) segment of the chain and, in turn, consider the conditions that support its escape and collapse of the chain. Finally, our path from one to the few and finally to the many excited sites is completed by a modulational stability analysis and the exploration of its connection to the escape process for plane wave initial data. This reveals the existence of three distinct regimes, namely modulational stability, modulational instability without escape and, finally, modulational instability accompanied by escape. These are corroborated by direct numerical simulations. In each of the above cases, the variations of the relevant model parameters enable a consideration of the interplay of discreteness and nonlinearity within the observed phenomenology. (C) 2012 Elsevier B.V. All rights reserved.
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