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Asymptotic Approximation of Discrete Breather Modes in Two-Dimensional Lattices

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Quodons in Mica

Part of the book series: Springer Series in Materials Science ((SSMATERIALS,volume 221))

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Abstract

We outline the small amplitude asymptotic approximation for breathers for one-dimensional chains, and two-dimensional lattices with square, triangular/hexagonal, and honeycomb geometries. Two-dimensional lattices are complicated due to the resulting NLS-type equation being either elliptic or hyperbolic in nature. This gives rise to an additional constraint in addition to the usual condition on the relative strengths of quadratic and cubic nonlinearities. The honeycomb lattice requires a more advanced approach since it has a diatomic nature. Results from the three geometries are compared.

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Acknowledgments

I am grateful to Imran Butt and Lauren James, for their contributions to the work presented herein. I am also grateful to Mike Russell and Chris Eilbeck for interesting conversations and advice. I would like to thank Juan Archilla for organising the excellent meeting in Altea in September 2013.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK

    Jonathan A. D. Wattis

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  1. Jonathan A. D. Wattis
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Correspondence to Jonathan A. D. Wattis .

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Editors and Affiliations

  1. Departamento de Física Aplicada I, Group of Nonlinear Physics, Universidad de Sevilla, Sevilla, Spain

    Juan F. R. Archilla

  2. Física Aplicada, EPS Gandía, Universidad Politécnica de Valencia, Gandia, Spain

    Noé Jiménez

  3. Física Aplicada, EPS Gandia, Universidad Politécnica de Valencia, Gandia, Spain

    Victor J. Sánchez-Morcillo

  4. Matemática Aplicada, Universidad Politécnica de Valencia, Valencia, Spain

    Luis M. García-Raffi

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Wattis, J.A.D. (2015). Asymptotic Approximation of Discrete Breather Modes in Two-Dimensional Lattices. In: Archilla, J., Jiménez, N., Sánchez-Morcillo, V., García-Raffi, L. (eds) Quodons in Mica. Springer Series in Materials Science, vol 221. Springer, Cham. https://doi.org/10.1007/978-3-319-21045-2_7

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