Nonlinear layered lattice model and generalized solitary waves in imperfectly bonded structures
journal contributionposted on 02.09.2014 by Karima Khusnutdinova, Alexander M. Samsonov, Alexey S. Zakharov
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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.
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.
- Mathematical Sciences