### Abstract

The existence of longitudinal periodic permanent waves in a one-dimensional translationally invariant anharmonic chain with nearest-neighbour interaction is established by means of variational methods. A general expression for the energy is given in terms of the dispersion relation. The interaction potential is not specified in detail. Fundamental assumptions are: the potential has a vertical asymptote for small distance and a horizontal one for large distance between two neighbouring particles. In the limit for high energy the wave looks like an infinite series of 'spikes' with finite amplitude and 'infinite' velocity

Original language | English |
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Pages (from-to) | 1885-1897 |

Journal | Journal of physics A: mathematical and general |

Volume | 11 |

Issue number | 10 |

DOIs | |

Publication status | Published - 1978 |

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## Cite this

Valkering, T. P. (1978). Periodic permanent waves in an anharmonic chain with nearest-neighbour interaction.

*Journal of physics A: mathematical and general*,*11*(10), 1885-1897. https://doi.org/10.1088/0305-4470/11/10/008