中国物理B ›› 2008, Vol. 17 ›› Issue (8): 2989-2993.doi: 10.1088/1674-1056/17/8/038

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The interaction of nonlinear waves in two-dimensional lattice

杨晓霞, 段文山, 栗生长, 韩久宁   

  1. College of Physics and Electronics Engineering, Northwest Normal University, Lanzhou 730070, China
  • 收稿日期:2007-10-28 修回日期:2007-11-27 出版日期:2008-08-20 发布日期:2008-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China under (Grant Nos 10575082 and 10247008), the Scientific Research Foundation (SRF) for the Returned Overseas Chinese Scholars (ROCF), State Education Ministry (SEM).

The interaction of nonlinear waves in two-dimensional lattice

Yang Xiao-Xia(杨晓霞), Duan Wen-Shan(段文山)†, Li Sheng-Chang(栗生长), and Han Jiu-Ning(韩久宁)   

  1. College of Physics and Electronics Engineering, Northwest Normal University, Lanzhou 730070, China
  • Received:2007-10-28 Revised:2007-11-27 Online:2008-08-20 Published:2008-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China under (Grant Nos 10575082 and 10247008), the Scientific Research Foundation (SRF) for the Returned Overseas Chinese Scholars (ROCF), State Education Ministry (SEM).

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摘要： This paper investigates the collision between two nonlinear waves with arbitrary angle in two-dimensional nonlinear lattice. By using the extended Poincar\'{e}--Lighthill--Kuo perturbation method, it obtains two Korteweg--de Vries equations for nonlinear waves in both the $\xi$ and $\eta$ directions, respectively, and derives the analytical phase shifts after the collision of two nonlinear waves. Finally, the solution of $u(v)$ up to $O(\epsilon^{3})$ order is given.

关键词: nonlinear waves, two-dimensional nonlinear lattice, phase shift

Abstract: This paper investigates the collision between two nonlinear waves with arbitrary angle in two-dimensional nonlinear lattice. By using the extended Poincaré--Lighthill--Kuo perturbation method, it obtains two Korteweg--de Vries equations for nonlinear waves in both the $\xi$ and $\eta$ directions, respectively, and derives the analytical phase shifts after the collision of two nonlinear waves. Finally, the solution of $u(v)$ up to $O(\epsilon^{3})$ order is given.

Key words: nonlinear waves, two-dimensional nonlinear lattice, phase shift

中图分类号:  (Solitons)

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