Weakly nonlinear localization for a 1-D FPU chain with clustering zones

• Published in: The European physical journal. ST, Special topics Special topics, 2014-12, Vol.223 (13), p.2943-2952
• Main Authors: Martínez-Farías, F., Panayotaros, P., Olvera, A.
• Format: Article
• Language: English
• Subjects: Advanced Computational and Experimental Techniques in Nolinear Dynamics. Guest Editors: Elbert E.N. Macau and Carlos L. Pando Lambruschini (Eds.); Atomic; Classical and Continuum Physics; Condensed Matter Physics; Materials Science; Measurement Science and Instrumentation; Molecular; Optical and Plasma Physics; Physics; Physics and Astronomy; Regular Article
• ISSN: 1951-6355; 1951-6401
• DOI: 10.1140/epjst/e2014-02307-7

We study weakly nonlinear spatially localized solutions of a Fermi-Pasta-Ulam model describing a unidimensional chain of particles interacting with a number of neighbors that can vary from site to site. The interaction potential contains quadratic and quartic terms, and is derived from a nonlinear elastic network model proposed by Juanico et al. [1]. The FPU model can be also derived for arbitrary dimensions, under a small angular displacement assumption. The variable interaction range is a consequence of the spatial inhomogeneity in the equilibrium particle distribution. We here study some simple one-dimensional examples with only a few, well defined agglomeration regions. These agglomerations are seen to lead to spatially localized linear modes and gaps in the linear spectrum, which in turn imply a normal form that has spatially localized periodic orbits.