中国物理B ›› 2009, Vol. 18 ›› Issue (6): 2352-2358.doi: 10.1088/1674-1056/18/6/039

• CLASSICAL AREAS OF PHENOMENOLOGY • 上一篇    下一篇

Solutions to the equations describing materials with competing quadratic and cubic nonlinearities

赵丽娜1, 林机1, 童子双2   

  1. (1)Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China; (2)Normal School, Jinhua College of Profession and Technology, Jinhua 321017, China
  • 收稿日期:2008-08-20 修回日期:2009-01-12 出版日期:2009-06-20 发布日期:2009-06-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10575087 and 10875106).

Solutions to the equations describing materials with competing quadratic and cubic nonlinearities

Zhao Li-Na(赵丽娜)a), Tong Zi-Shuang(童子双)b), and Lin Ji(林机)a)†   

  1. a Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua 321004, China; b Normal School, Jinhua College of Profession and Technology, Jinhua 321017, China
  • Received:2008-08-20 Revised:2009-01-12 Online:2009-06-20 Published:2009-06-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos 10575087 and 10875106).

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摘要： The Lie group theoretical method is used to study the equations describing materials with competing quadratic and cubic nonlinearities. The equations share some of the nice properties of soliton equations. From the elliptic functions expansion method, we obtain large families of analytical solutions, in special cases, we have the periodic, kink and solitary solutions of the equations. Furthermore, we investigate the stability of these solutions under the perturbation of amplitude noises by numerical simulation.

Abstract: The Lie group theoretical method is used to study the equations describing materials with competing quadratic and cubic nonlinearities. The equations share some of the nice properties of soliton equations. From the elliptic functions expansion method, we obtain large families of analytical solutions, in special cases, we have the periodic, kink and solitary solutions of the equations. Furthermore, we investigate the stability of these solutions under the perturbation of amplitude noises by numerical simulation.

Key words: competing nonlinearities, the elliptic functions expansion, soliton, numerical simulation

中图分类号:  (Optical solitons; nonlinear guided waves)

  • 42.65.Tg
02.20.Sv (Lie algebras of Lie groups) 02.60.-x (Numerical approximation and analysis) 42.70.Nq (Other nonlinear optical materials; photorefractive and semiconductor materials)