中国物理B ›› 2000, Vol. 9 ›› Issue (2): 81-85.doi: 10.1088/1009-1963/9/2/001

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PARTICULAR SOLITONS IN NONLINEAR LATTICE

吕克璞1, 段文山1, 赵金保1, 王本仁2, 魏荣爵2   

  1. (1)Department of Physics, Northwest Normal University, Lanzhou 730070, China; (2)Institute of Acoustics, Nanjing University, Nanjing 210093, China
  • 收稿日期:1998-12-23 修回日期:1999-05-18 出版日期:2000-02-15 发布日期:2005-06-10
  • 基金资助:
    Project supported by the Natural Science Foundation of Gansu Province, China (Grant No. ZS981-A25-008-Z).

PARTICULAR SOLITONS IN NONLINEAR LATTICE

Lü Ke-pu (吕克璞)a, Duan Wen-shan (段文山)a, Zhao Jin-bao (赵金保)a, Wang Ben-ren (王本仁)b, Wei Rong-jue (魏荣爵)b   

  1. a Department of Physics, Northwest Normal University, Lanzhou 730070, China; b Institute of Acoustics, Nanjing University, Nanjing 210093, China
  • Received:1998-12-23 Revised:1999-05-18 Online:2000-02-15 Published:2005-06-10
  • Supported by:
    Project supported by the Natural Science Foundation of Gansu Province, China (Grant No. ZS981-A25-008-Z).

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摘要： One soliton of particle velocity and its amplitude (maximum particle velocity of one soliton) in Toda lattice is given analytically. It has also been known numerically that the maximum particle velocity (when the collision of two solitons reaches their maximum, we define Vn at this time as its maximum particle velocity) during the collision of two solitons moving in the same direction is equal to the difference between the amplitudes of two solitons if the difference is large enough; however, the maximum particle velocity is equal to the adding up of the amplitudes of two solitons moving in the opposite directions. The relationship between the maximum value of e-(rn)-1 and their initial amplitude of e-(rn)-1 is also given analytically in Toda lattice if the amplitudes of the two solitons are the same and their moving directions are opposite. Compared with the Boussinesq equation, there are differences between the Toda lattice equation and the Boussinesq equation for solitons during the collision.

Abstract: One soliton of particle velocity and its amplitude (maximum particle velocity of one soliton) in Toda lattice is given analytically. It has also been known numerically that the maximum particle velocity (when the collision of two solitons reaches their maximum, we define Vn at this time as its maximum particle velocity) during the collision of two solitons moving in the same direction is equal to the difference between the amplitudes of two solitons if the difference is large enough; however, the maximum particle velocity is equal to the adding up of the amplitudes of two solitons moving in the opposite directions. The relationship between the maximum value of e-rn-1 and their initial amplitude of e-rn-1 is also given analytically in Toda lattice if the amplitudes of the two solitons are the same and their moving directions are opposite. Compared with the Boussinesq equation, there are differences between the Toda lattice equation and the Boussinesq equation for solitons during the collision.

中图分类号:  (Solitons)

  • 05.45.Yv
05.50.+q (Lattice theory and statistics)