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Breathers on lattices with long range interaction

S. Flach
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Abstract

We analyze the properties of breathers (time periodic spatially localized solutions) on chains in the presence of algebraically decaying interactions $1/r^s$. We find that the spatial decay of a breather shows a crossover from exponential (short distances) to algebraic (large distances) decay. We calculate the crossover distance as a function of $s$ and the energy of the breather. Next we show that the results on energy thresholds obtained for short range interactions remain valid for $s>3$ and that for $s < 3$ (anomalous dispersion at the band edge) nonzero thresholds occur for cases where the short range interaction system would yield zero threshold values.

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S. Flach. 1998-09-29. Breathers on lattices with long range interaction. https://doi.org/10.1103/physreve.58.r4116

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