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Solitary Waves for Nonconvex FPU Lattices

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Abstract

Solitary waves in a one-dimensional chain of atoms \(\{q_j\}_{j\in{\Bbb Z}}\) are investigated. The potential energy is required to be monotone and grow super-quadratically. The existence of solitary waves with a prescribed asymptotic strain is shown under certain assumptions on the asymptotic strain and the wave speed. It is demonstrated that the invariance of the equations allows one to transform a system with nonconvex potential energy density to the situation under consideration.

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Authors and Affiliations

  1. Mathematical Sciences, University of Bath, Bath BA2 7AY, UK

    Hartmut Schwetlick & Johannes Zimmer

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  1. Hartmut Schwetlick
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  2. Johannes Zimmer
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Correspondence to Hartmut Schwetlick or Johannes Zimmer.

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Schwetlick, H., Zimmer, J. Solitary Waves for Nonconvex FPU Lattices. J Nonlinear Sci 17, 1–12 (2007). https://doi.org/10.1007/s00332-005-0735-0

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  • DOI: https://doi.org/10.1007/s00332-005-0735-0

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