×

Breather initial profiles in chains of weakly coupled anharmonic oscillators. (English) Zbl 0996.70017

Summary: A systematic correlation between the initial profile of discrete breathers and their frequency is described. The context is that of a very weakly harmonically coupled chain of softly anharmonic oscillators. The results are structurally stable, that is, robust under changes of the on-site potential, and are illustrated numerically for several standard choices. A precise genericity theorem for the results is proved.

MSC:

70K20 Stability for nonlinear problems in mechanics
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[1] Flach, S.; Willis, C.R., Phys. rep., 295, 181, (1998)
[2] MacKay, R.S.; Aubry, S., Nonlinearity, 7, 1623, (1994)
[3] Marı́n, J.L.; Aubry, S., Nonlinearity, 9, 1501, (1996)
[4] Bountis, T.; Capel, H.W.; Kollmann, M.; Ross, J.C.; Bergamin, J.M.; van der Weele, J.P., Phys. lett. A, 268, 50, (2000)
[5] Haskins, M.; Speight, J.M., Nonlinearity, 11, 1651, (1998)
[6] Choquet-Bruhat, Y.; DeWitt-Morette, C.; Dillard-Bleick, M., Analysis, manifolds and physics, part I, (1982), North-Holland Amsterdam, p. 91
[7] Grimshaw, R., Nonlinear ordinary differential equations, (1990), Blackwell Scientific Publications Oxford, Chapter 7 · Zbl 0743.34002
[8] Flach, S., Phys. rev. E, 51, 3579, (1995)
[9] Prohofsky, E.W.; Lu, K.C.; Van Zandt, L.L.; Putnam, B.F., Phys. lett. A, 70, 492, (1979)
[10] Choquet-Bruhat, Y.; DeWitt-Morette, C.; Dillard-Bleick, M., Analysis, manifolds and physics, part I, (1982), North-Holland Amsterdam, p. 550
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.