Parametric Simultons in Nonlinear Lattices

Details Parametric Simultons in Nonlinear Lattices Parametric Simultons in Nonlinear Lattices

2000-06-28

arxiv.org/abs/cond-mat/0006444v1

Physics

Condensed Matter

14 pages in Revtex, no figure

Scientific paper

Parametric simultaneous solitary wave (simulton) excitations are shown possible in nonlinear lattices. Taking a one-dimensional diatomic lattice with a cubic potential as an example we consider the nonlinear coupling between the upper cutoff mode of acoustic branch (as a fundamental wave) and the upper cutoff mode of optical branch (as a second harmonic wave). Based on a quasi-discreteness approach the Karamzin-Sukhorukov equations for two slowly varying amplitudes of the fundamental and the second harmonic waves in the lattice are derived when the condition of second harmonic generation is satisfied. The lattice simulton solutions are explicitly given and the results show that these lattice simultons can be nonpropagating when the wave vectors of the fundamental wave and the second harmonic waves are exactly at $\pi/a$ (where $a$ is the lattice constant) and zero, respectively.

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