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Exact discrete breather compactons in nonlinear Klein-Gordon lattices
1Physics Department, University of Crete and Foundation for Research and Technology-Hellas, P. O. Box 2208, 71003 Heraklion, Crete, Greece. comte@physics.uoc.gr
Summary
This study confirms exact discrete compact breather solutions in nonlinear Klein-Gordon systems. Breather stability depends on lattice boundaries, coupling, and harmonicity, expanding on prior research.
Area of Science:
- Nonlinear dynamics
- Condensed matter physics
- Mathematical physics
Background:
- Nonlinear Klein-Gordon systems are crucial for modeling various physical phenomena.
- Discrete compact breathers are localized, time-periodic solutions with potential applications.
- Previous work by Tchofo Dinda and Remoissenet laid groundwork for breather analysis.
Purpose of the Study:
- To demonstrate the existence of exact discrete compact breather solutions in nonlinear Klein-Gordon systems.
- To elucidate the primary factors governing the stability of these breather solutions.
- To extend and complete the findings of Tchofo Dinda and Remoissenet (1999).
Main Methods:
- Analytical investigation of nonlinear Klein-Gordon equations.
- Derivation and characterization of discrete compact breather solutions.
- Stability analysis focusing on lattice parameters and coupling terms.
Main Results:
- Confirmed the existence of exact discrete compact breather solutions.
- Identified lattice boundary conditions as a principal factor in breather stability.
- Established the roles of the coupling term and harmonicity parameter in stability.
Conclusions:
- The stability of discrete compact breathers is intricately linked to specific system parameters.
- This research provides a more complete understanding of breather dynamics in discrete nonlinear systems.
- Findings offer insights for controlling and utilizing localized nonlinear excitations.