中国物理B ›› 2001, Vol. 10 ›› Issue (6): 523-530.doi: 10.1088/1009-1963/10/6/312

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PARAMETRIC SIMULTONS IN ONE-DIMENSIONAL NONLINEAR LATTICES

黄国翔   

  1. Department of Physics and State Key Laboratory of Optical and Magnetic Resonance Spectroscopy, East China Normal University, Shanghai 200062, China
  • 收稿日期:2000-05-09 修回日期:2000-07-24 出版日期:2001-06-15 发布日期:2005-06-12
  • 基金资助:
    Project supported in part by the National Natural Science Foundation of China (Grant No. 19975019), by the Trans-Century Training Programme Foundation for the Talents of the Ministry of Education, China.

PARAMETRIC SIMULTONS IN ONE-DIMENSIONAL NONLINEAR LATTICES

Huang Guo-xiang (黄国翔)   

  1. Department of Physics and State Key Laboratory of Optical and Magnetic Resonance Spectroscopy, East China Normal University, Shanghai 200062, China
  • Received:2000-05-09 Revised:2000-07-24 Online:2001-06-15 Published:2005-06-12
  • Supported by:
    Project supported in part by the National Natural Science Foundation of China (Grant No. 19975019), by the Trans-Century Training Programme Foundation for the Talents of the Ministry of Education, China.

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摘要： Parametric simultaneous solitary wave (simulton) excitations are shown to be 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 cut-off mode of acoustic branch (as a fundamental wave) and the upper cut-off 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 given explicitly 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 π/a (where a is the lattice constant) and zero, respectively.

Abstract: Parametric simultaneous solitary wave (simulton) excitations are shown to be 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 cut-off mode of acoustic branch (as a fundamental wave) and the upper cut-off 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 given explicitly 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.

Key words: nonlinear lattice waves, solitons, simultons

中图分类号:  (Solitons)

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