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Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures

Karima R. Khusnutdinova1,*, Alexander M. Samsonov2, and Alexey S. Zakharov1

  • 1Department of Mathematical Sciences, Loughborough University, Loughborough LE11 3TU, United Kingdom
  • 2Ioffe Physico-Technical Institute of the Russian Academy of Sciences, St. Petersburg 194021, Russia

  • *Corresponding author: FAX: +44 (0)1509 223969; k.khusnutdinova@lboro.ac.uk
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Phys. Rev. E 79, 056606 – Published 13 May, 2009

DOI: https://doi.org/10.1103/PhysRevE.79.056606

Abstract

We study nonlinear waves in a two-layered imperfectly bonded structure using a nonlinear lattice model. The key element of the model is an anharmonic chain of oscillating dipoles, which can be viewed as a basic lattice analog of a one-dimensional macroscopic waveguide. Long nonlinear longitudinal waves in a layered lattice with a soft middle (or bonding) layer are governed by a system of coupled Boussinesq-type equations. For this system we find conservation laws and show that pure solitary waves, which exist in a single equation and can exist in the coupled system in the symmetric case, are structurally unstable and are replaced with generalized solitary waves.

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Phys. Rev. E 79, 056606– Published 13 May, 2009
  • Received 21 November 2008

© 2009 American Physical Society

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