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Nonlinear long-wave models for imperfectly bonded layered waveguides

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Abstract

We propose a composite lattice model for describing nonlinear waves in a two-layer waveguide with adhesive bonding. We first consider waves in an anharmonic chain of oscillating dipoles and show that the corresponding asymptotic long-wave model for longitudinal waves coincides with the Boussinesq-type equation previously derived for a macroscopic waveguide using the nonlinear elasticity approach. We also show that in this model, there is no simple analogy between long longitudinal and long flexural waves. Then, for a composite lattice, we derive two new model systems of coupled Boussinesq-type equations for long nonlinear longitudinal waves and conjecture that a similar description exists in the framework of dynamic nonlinear elasticity.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Loughborough University, Loughborough, UK

    K. R. Khusnutdinova & A. S. Zakharov

  2. Ioffe Physico-Technical Institute, RAS, St. Petersburg, Russia

    A. M. Samsonov

Authors
  1. K. R. Khusnutdinova
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  2. A. M. Samsonov
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  3. A. S. Zakharov
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Corresponding author

Correspondence to K. R. Khusnutdinova.

Additional information

Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 159, No. 3, pp. 475–489, June, 2009.

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Khusnutdinova, K.R., Samsonov, A.M. & Zakharov, A.S. Nonlinear long-wave models for imperfectly bonded layered waveguides. Theor Math Phys 159, 819–832 (2009). https://doi.org/10.1007/s11232-009-0070-y

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