Scaling properties of $q$-breathers in nonlinear acoustic lattices

Details Scaling properties of $q$-breathers in nonlinear acoustic lattices Scaling properties of $q$-breathers in nonlinear acoustic lattices

2006-07-11

arxiv.org/abs/nlin/0607019v1

Nonlinear Sciences

Pattern Formation and Solitons

4 pages, 5 figures

Scientific paper

10.1016/j.physleta.2007.01.056

Recently $q$-breathers - time-periodic solutions which localize in the space of normal modes and maximize the energy density for some mode vector $q_0$ - were obtained for finite nonlinear lattices. We scale these solutions together with the size of the system to arbitrarily large lattices. We generalize previously obtained analytical estimates of the localization length of $q$-breathers. The first finding is that the degree of localization depends only on intensive quantities and is size independent. Secondly a critical wave vector $k_m$ is identified, which depends on one effective nonlinearity parameter. $q$-breathers minimize the localization length at $k_0=k_m$ and completely delocalize in the limit $k_0 \to 0$.

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