| 白永强,裴明,刘震.差分方程拉克斯对的一种构造性方法[J].数学年刊A辑,2014,35(5):583~590 |
| 差分方程拉克斯对的一种构造性方法 |
| A Constructive Method for the Lax Pair of Difference Equations |
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| DOI： |
| 中文关键词: 非交换微分, 差分方程, 拉克斯对 |
| 英文关键词:Noncommutative differential calculus, Difference equation, Lax pair |
| 基金项目:国家自然科学基金 (No.10801045) |
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| 中文摘要: |
| 非交换微分在讨论数学物理中的偏微分方程时起着十分重要的作用.最近，
作者利用一个具体的非交换外微分建立了一种求差分微分方程拉克斯对的方法，
由此检验了该方程的可积性. 本文给出了讨论全差分方程的对应理论. 另外还讨论了
一个格子形变的KdV (LMKdV)方程，并求得了它的拉克斯对. |
| 英文摘要: |
| Noncommutative differential calculus plays a
fundamental role in discussing partial differential equations
in mathematical physics. Recently, the authors have used a concrete
noncommutative exterior differential calculus to develop a theory
of the Lax pair of differential-difference equations and
thus test their integrability. In this paper, a
discrete theory is proposed to discuss difference equations. In addition, a
lattice modified Korteweg-de Vries (LMKdV for short) is discussed and the
corresponding Lax pairs are also given. |
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