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Travelling waves in microstructure as the exact solutions to the 6th order nonlinear equation

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Abstract

The travelling wave solutions to the nonlinear partial differential equation of 6th order are obtained for a solid having two different spatial scales introduced in the microstructure. The slaving principle method is applied, and the exact explicit solution is found in terms of the doubly periodic Weierstrass elliptic function for the corresponding ODE. Several particular cases are discussed for various parameter values, e.g., the solitary “mexican hat” pulse is found with polarity, depending on microstructure parameters.

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Authors and Affiliations

  1. Department of Mathematics, University of Torino, Torino, 10123, Italy

    A. Casasso & F. Pastrone

  2. The Ioffe Physical Technical Institute of the Russian Academy of Sciences, St. Petersburg, 194021, Russia

    A. M. Samsonov

Authors
  1. A. Casasso
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  2. F. Pastrone
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  3. A. M. Samsonov
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Correspondence to F. Pastrone.

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Casasso, A., Pastrone, F. & Samsonov, A.M. Travelling waves in microstructure as the exact solutions to the 6th order nonlinear equation. Acoust. Phys. 56, 871–876 (2010). https://doi.org/10.1134/S1063771010060114

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  • DOI: https://doi.org/10.1134/S1063771010060114

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