The superlattices of discrete breathers in the model of the 1D crystal

Accepted: 22 January 2016
Citation: D.V. Laptev. The superlattices of discrete breathers in the model of the 1D crystal. Letters on Materials, 2016, 6(1) 34-38
BibTex   DOI: 10.22226/2410-3535-2016-1-34-38

Abstract

The dynamics of the single discrete breathers and discrete breathers superlattices for the model of the 1D anharmonic Hirota lattice and equivalent nonlinear transmission line described by the system of nonlinear self-dual network equations has been considered. The periodic and zero-fixed boundary conditions were used for the arbitrary number of sites. The analogues of the discrete breather for the finite-size system with periodic boundary conditions are presented. For the analogue of the discrete breather for the finite-size system the linear stability has been investigated. Using the generalized Hirota lattice model the influence of the dissipation on the dynamics have been discussed. Using the exact discrete breathers superlattices solutions of the Hirota lattice equation the asymptotic interaction energy between two breathers has been investigated. It was shown that the character of interaction of breathers in the superlattice of type I oscillating in the opposite phase is repulsion. On the other hand breathers in the superlattice of type II oscillating in the same phase attract each other. For large separation of breathers the energies of superlattices of both types reduce to sum of the energies of free discrete breathers. For small separation of breathers the energy of superlattice of type I tends to the energy of the homogeneous anti-phase oscillations and the energy of superlattice of type II tends to zero.

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