Cauchy problem for integrable discrete equations on quad-graphs

被引：29
|
作者：
Adler, VE
Veselov, AP
机构：
[1] Tech Univ Berlin, Inst Math, D-10623 Berlin, Germany
[2] Univ Loughborough, Loughborough LE11 3TU, Leics, England
来源：
ACTA APPLICANDAE MATHEMATICAE | 2004年 / 84卷 / 02期
关键词：
Cauchy problem; quad-graph; discrete integrable equations;
D O I：
10.1007/s10440-004-5557-9
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Initial value problems for the integrable discrete equations on quad-graphs are investigated. We give a geometric criterion of when such a problem is well-posed. In the basic example of the discrete KdV equation an effective integration scheme based on the matrix factorization problem is proposed and the interaction of the solutions with the localized defects in the regular square lattice are discussed in details. The examples of kinks and solitons on various quad-graphs, including quasiperiodic tilings, are presented.
引用
收藏
页码：237 / 262
页数：26
相关论文
共 50 条
  • [1] Cauchy Problem for Integrable Discrete Equations on Quad-Graphs
    V. E. Adler
    A. P. Veselov
    Acta Applicandae Mathematica, 2004, 84 : 237 - 262
  • [2] Classification of Integrable Boundary Equations for Integrable Systems on Quad-Graphs
    Sun, Pengyu
    Zhang, Cheng
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2023, 2023 (16) : 13601 - 13657
  • [3] Integrable systems on quad-graphs
    Bobenko, AI
    Suris, YB
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2002, 2002 (11) : 573 - 611
  • [4] Linear Integrable Systems on Quad-Graphs
    Bobenko, Alexander, I
    Suris, Yuri B.
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2022, 2022 (19) : 14639 - 14674
  • [5] Yang-Baxter maps and symmetries of integrable equations on quad-graphs
    Papageorgiou, Vassilios G.
    Tongas, Anastasios G.
    Veselov, Alexander P.
    JOURNAL OF MATHEMATICAL PHYSICS, 2006, 47 (08)
  • [6] Non-symmetric discrete Toda systems from quad-graphs
    Boll, Raphael
    Suris, Yuri B.
    APPLICABLE ANALYSIS, 2010, 89 (04) : 547 - 569
  • [7] Rhombic embeddings of planar quad-graphs
    Kenyon, R
    Schlenker, JM
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 357 (09) : 3443 - 3458
  • [8] Quasi-classical expansion of the star-triangle relation and integrable systems on quad-graphs
    Bazhanov, Vladimir V.
    Kels, Andrew P.
    Sergeev, Sergey M.
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2016, 49 (46)
  • [9] Classification of Integrable Equations on Quad-Graphs. The Consistency Approach
    V.E. Adler
    A.I. Bobenko
    Yu.B. Suris
    Communications in Mathematical Physics, 2003, 233 : 513 - 543
  • [10] Integrable noncommutative equations on quad-graphs. The consistency approach
    Bobenko, AI
    Suris, YB
    LETTERS IN MATHEMATICAL PHYSICS, 2002, 61 (03) : 241 - 254
12345