THE DISCRETE KORTEWEG-DE VRIES EQUATION

被引：204
|
作者：
NIJHOFF, F
CAPEL, H
机构：
[1] UNIV AMSTERDAM, INST THEORET PHYS, 1018 XE AMSTERDAM, NETHERLANDS
[2] UNIV LEEDS, DEPT APPL MATH SCI, LEEDS LS2 9JT, W YORKSHIRE, ENGLAND
来源：
ACTA APPLICANDAE MATHEMATICAE | 1995年 / 39卷 / 1-3期
关键词：
LATTICE EQUATIONS; LINEARIZATION; DISCRETIZATION; MIURA TRANSFORMATIONS; SIMILARITY REDUCTIONS;
D O I：
10.1007/BF00994631
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We review the different aspects of integrable discretizations in space and time of the Korteweg-de Vries equation, including Miura transformations to related integrable difference equations, connections to integrable mappings, similarity reductions and discrete versions of Painleve equations as well as connections to Volterra systems.
引用
收藏
页码：133 / 158
页数：26
相关论文
共 50 条
  • [1] Conservation Laws of Discrete Korteweg-de Vries Equation
    Rasin, Olexandr G.
    Hydon, Peter E.
    [J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2005, 1
  • [2] KORTEWEG-DE VRIES EQUATION
    SHABAT, AB
    [J]. DOKLADY AKADEMII NAUK SSSR, 1973, 211 (06): : 1310 - 1313
  • [3] KORTEWEG-DE VRIES EQUATION
    TSUTSUMI, M
    [J]. PROCEEDINGS OF THE JAPAN ACADEMY, 1975, 51 (06): : 399 - 401
  • [4] Boundary Stabilization of the Korteweg-de Vries Equation and the Korteweg-de Vries-Burgers Equation
    Chaohua Jia
    Bing-Yu Zhang
    [J]. Acta Applicandae Mathematicae, 2012, 118 : 25 - 47
  • [5] Boundary Stabilization of the Korteweg-de Vries Equation and the Korteweg-de Vries-Burgers Equation
    Jia, Chaohua
    Zhang, Bing-Yu
    [J]. ACTA APPLICANDAE MATHEMATICAE, 2012, 118 (01) : 25 - 47
  • [6] Integrability of reductions of the discrete Korteweg-de Vries and potential Korteweg-de Vries equations
    Hone, A. N. W.
    van der Kamp, P. H.
    Quispel, G. R. W.
    Tran, D. T.
    [J]. PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2013, 469 (2154):
  • [7] Integrability and solutions of a nonsymmetric discrete Korteweg-de Vries equation
    Maebel Mesfun
    Da-jun Zhang
    Song-lin Zhao
    [J]. Communications in Theoretical Physics, 2024, 76 (02) : 47 - 52
  • [8] Integrability and solutions of a nonsymmetric discrete Korteweg-de Vries equation
    Mesfun, Maebel
    Zhang, Da-jun
    Zhao, Song-lin
    [J]. COMMUNICATIONS IN THEORETICAL PHYSICS, 2024, 76 (02)
  • [9] KORTEWEG-DE VRIES EQUATION AND GENERALIZATIONS .3. DERIVATION OF KORTEWEG-DE VRIES EQUATION AND BURGERS EQUATION
    SU, CH
    GARDNER, CS
    [J]. JOURNAL OF MATHEMATICAL PHYSICS, 1969, 10 (03) : 536 - &
  • [10] Discrete Negative Order Potential Korteweg-de Vries Equation
    Zhao, Song-lin
    Sun, Ying-ying
    [J]. ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2016, 71 (12): : 1151 - 1158
12345