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Compactlike discrete breathers in systems with nonlinear and nonlocal dispersive terms
1Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzerstr. 38, Dresden 01187, Germany.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 31, 2005
Summary
Discrete breathers with short-range interactions localize compactly. Adding long-range interactions creates competition, breaking compactness and introducing crossover lengths for these localized excitations.
Area of Science:
- Nonlinear physics
- Condensed matter physics
- Mathematical physics
Background:
- Discrete breathers are localized nonlinear excitations in periodic structures.
- Anharmonic interactions are crucial for breather formation and properties.
- Understanding localization and stability is key to their applications.
Purpose of the Study:
- To analyze spatial localization and dynamical stability of discrete breathers.
- To investigate the impact of both short- and long-range anharmonic interactions.
- To identify connections with known localized modes like compactons.
Main Methods:
- Analysis of spatial localization properties.
- Investigation of dynamical stability.
- Identification of solution branches and their connections to existing models.
Main Results:
- Purely short-range anharmonic interactions lead to superexponential localization and compact-like behavior.
- Connections established with Page-Sievers-Takeno lattice modes and Rosenau's compacton solutions.
- Absence of linear dispersion enables extremely long-lived, time-quasiperiodic localized excitations.
- Inclusion of long-range anharmonic interactions introduces competition between length scales.
- Competition results in characteristic crossover lengths, breaking the compactness concept.
Conclusions:
- Discrete breathers exhibit diverse localization behaviors depending on interaction range.
- Long-range interactions significantly modify breather properties, challenging the notion of compactness.
- The interplay of short- and long-range forces leads to complex spatial structures and dynamics.
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