Cauchy Problem for Integrable Discrete Equations on Quad-Graphs

被引：0
|
作者：
V. E. Adler
A. P. Veselov
机构：
[1] Technische Universität Berlin,Institut für Mathematik
[2] Loughborough University,undefined
[3] Loughborough,undefined
[4] Leicestershire LE11 3TU,undefined
[5] UK and Landau Institute for Theoretical Physics,undefined
来源：
Acta Applicandae Mathematica | 2004年 / 84卷
关键词：
Cauchy problem; quad-graph; discrete integrable equations;
D O I：
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中图分类号：
学科分类号：
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.
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页码：237 / 262
页数：25
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