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

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journal contribution
posted on 02.09.2014, 10:18 by Karima Khusnutdinova, Alexander M. Samsonov, Alexey S. Zakharov
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.

Funding

We thank E.S. Benilov, R.H.J. Grimshaw and A.B. Movchan for useful discussions. The research was supported by the UK EPSRC under Grant No. EP/D035570/1.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics

Volume

79

Pages

Art No. 056606 - ?

Citation

KHUSNUTDINOVA, K.R., SAMSONOV, A.M. and ZAKHAROV, A.S., 2009. Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures. Physical Review E, 79, 056606, 14pp.

Publisher

© American Physical Society

Version

VoR (Version of Record)

Publication date

2009

ISSN

1539-3755

Language

en

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