On the shapes of two-dimensional soliton perturbations in simple lattices

被引：0
|
作者：
Popov, S. P. [1 ]
机构：
[1] Russian Acad Sci, Dorodnicyn Comp Ctr, Moscow 119333, Russia
来源：
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS | 2009年 / 49卷 / 02期
关键词：
two-dimensional Toda lattice; discrete Korteweg-de Vries equation; integrable dynamical system; soliton; numerical solution;
D O I：
10.1134/S0965542509020110
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
The Toda lattice and the discrete Korteweg-de Vries equation generalized to two dimensions are studied numerically. The interactions are assumed to be identical in both directions. It is shown that the equations have solutions in the form of plane linear and localized solitons. In contrast to equations integrable by the inverse scattering method, the parameters of solitons change in the course of their interaction and additional wave structures are formed. The basic types of solutions characterizing these processes are presented.
引用
收藏
页码：314 / 322
页数：9
相关论文
共 50 条
  • [1] On the shapes of two-dimensional soliton perturbations in simple lattices
    S. P. Popov
    Computational Mathematics and Mathematical Physics, 2009, 49 : 314 - 322
  • [2] Soliton stripes in two-dimensional nonlinear photonic lattices
    Neshev, D
    Kivshar, YS
    Martin, H
    Chen, ZG
    OPTICS LETTERS, 2004, 29 (05) : 486 - 488
  • [3] Stable soliton complexes in two-dimensional photonic lattices
    Kartashov, YV
    Egorov, AA
    Torner, L
    Christodoulides, DN
    OPTICS LETTERS, 2004, 29 (16) : 1918 - 1920
  • [4] Symmetric and antisymmetric soliton states in two-dimensional photonic lattices
    Lou, CB
    Xu, JJ
    Tang, LQ
    Chen, ZG
    Kevrekidis, PG
    OPTICS LETTERS, 2006, 31 (04) : 492 - 494
  • [5] Dispersion relation for two-dimensional simple cubic lattices
    Tian, Dou-xiang
    Wang, Xiao-yun
    Wang, Cang-long
    Duan, Wen-shan
    FRONTIERS OF PHYSICS IN CHINA, 2008, 3 (02): : 159 - 164
  • [6] Dispersion relation for two-dimensional simple cubic lattices
    Dou-xiang Tian
    Xiao-yun Wang
    Cang-long Wang
    Wen-shan Duan
    Frontiers of Physics in China, 2008, 3 : 159 - 164
  • [7] Soliton-like excitations and solectrons in two-dimensional nonlinear lattices
    Chetverikov, A. P.
    Ebeling, W.
    Velarde, M. G.
    EUROPEAN PHYSICAL JOURNAL B, 2011, 80 (02): : 137 - 145
  • [8] Soliton Theory of Two-Dimensional Lattices: The Discrete Nonlinear Schrodinger Equation
    Arevalo, Edward
    PHYSICAL REVIEW LETTERS, 2009, 102 (22)
  • [9] Chaotic spatial soliton rays in smooth two-dimensional optical lattices
    Khomeriki, R.
    Leon, J.
    OPTICS LETTERS, 2009, 34 (21) : 3376 - 3378
  • [10] Soliton-like excitations and solectrons in two-dimensional nonlinear lattices
    A. P. Chetverikov
    W. Ebeling
    M. G. Velarde
    The European Physical Journal B, 2011, 80 : 137 - 145
12345