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

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 \[ H=\sum_n \Biggl[ \frac{P_n^2}{2}+ V(u_n)+ \frac{c}{2} (u_{n+1}- u_n)^2 \Biggr]. \]


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
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[1] Cretegny, T.; Aubry, S.; Flach, S., Physica D, 119, 73-87, (1998)
[2] Sievers, A.J.; Takeno, S., Phys. rev. lett., 61, 970, (1988)
[3] Flach, S.; Willis, C.R., Phys. rep., 295, 181-246, (1998)
[4] MacKay, R.S.; Aubry, S., Nonlinearity, 7, 1623-1643, (1994)
[5] Marín, J.L.; Aubry, S., Nonlinearity, 9, 1501-1528, (1996)
[6] Arnold, V.I., Mathematical methods of classical mechanics, (1989), Springer Berlin
[7] Marín, J.L.; Aubry, S.; Floría, L.M., (), Physica D, to appear
[8] Marín, J.L., ()
[9] available at http://wanda.unizar.es/marin/PhDthesis, and upon request from the author.
[10] Aubry, S., Physica D, 103, 201-250, (1997)
[11] Campbell, D.K.; Peyrard, M.; Peyrard, M., (), Physica D, 119, 184-199, (1998)
[12] D.K. Campbell, M. Peyrard, private communication.
[13] Baesens, C.; Kim, S.; MacKay, R.S., Localised modes on coherent structures, Physica D, (1998), these proceedings · Zbl 0960.82003
[14] Johansson, M.; Aubry, S., Nonlinearity, 10, 1151-1178, (1997)
[15] Kittel, C.; Ashcroft, N.W.; Mermin, N.D., Solid state physics, (1976), Saunders College Philadelphia
[16] Magnus, W.; Winkler, S., Hill’s equation, (1966), Wiley, Inter-science New York · Zbl 0158.09604
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