Finite size effects on instabilities of discrete breathers. (English) Zbl 0942.37050

Marín, J. L.; Aubry, S.

Physica D 119, No. 1-2, 163-174 (1998).

The authors deal with one aspect of the stability of breathers which involves the size of the system. For numerical calculations, the authors consider finite systems with standard periodic boundary conditions. They illustrate their results by considering as an example the well-known one-dimensional Klein-Gordon model which consists of anharmonic oscillators with unity mass and harmonic nearest neighbor coupling with constant \(c\). Its Hamiltonian is \[ H=\sum_n \Biggl[ \frac{P_n^2}{2}+ V(u_n)+ \frac{c}{2} (u_{n+1}- u_n)^2 \Biggr]. \]

Reviewer: Messoud Efendiev (Berlin)

MSC:

37K45	Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35Q99	Partial differential equations of mathematical physics and other areas of application
65L99	Numerical methods for ordinary differential equations
70K99	Nonlinear dynamics in mechanics

Keywords:

stability of breathers; one-dimensional Klein-Gordon model; Hamiltonian

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