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Discrete breathers in vibroimpact chains: analytic solutions.

O V Gendelman¹, L I Manevitch

¹Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel. ovgend@tx.technion.ac.il

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 15, 2008

Summary

Researchers found exact solutions for discrete breathers in nonlinear chains using vibroimpact potentials. This provides a high-energy limit and benchmarks for testing approximate methods in discrete breather theory.

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Area of Science:

Nonlinear dynamics
Condensed matter physics
Mathematical physics

Background:

Discrete breathers are localized, nonlinear vibrational modes in discrete systems.
Understanding their behavior is crucial in various fields, including solid-state physics and mechanical engineering.
Existing models often rely on approximations, especially for high-energy regimes.

Purpose of the Study:

To derive exact analytic solutions for discrete breathers.
To investigate systems belonging to Klein-Gordon and Fermi-Pasta-Ulam universality classes.
To provide a framework for studying energy crossovers and validating approximate methods.

Main Methods:

Utilizing vibroimpact potentials to combine extreme nonlinearity with self-consistent forced linear models.
Developing exact analytical solutions based on these potentials.
Directly analyzing the crossover between high and low energy regimes.

Main Results:

Exact analytic solutions for discrete breathers in nonlinear oscillatory chains are presented.
The solutions are applicable to both Klein-Gordon and Fermi-Pasta-Ulam universality classes.
A direct study of the high- and low-energy crossover is enabled.

Conclusions:

The derived exact solutions offer a valuable high-energy limit for other realistic potentials.
These solutions serve as crucial benchmarks for testing approximate approaches in discrete breather theory.
The vibroimpact potential method provides a powerful tool for analyzing complex nonlinear systems.