上海大学学报(自然科学版)
• 数理化科学 • 上一篇
张海菲，张成，张大军
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通讯作者:
ZHANG Haifei, ZHANG Cheng, ZHANG Dajun
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摘要： 对可积偏微分方程Lax对作规范变换是拓展可积方程的重要工具。主要研究可积离散方程的规范变换。通过对离散Korteweg-de Vrier(KdV) 方程Lax对作两次规范变换，得到离散修正KdV与离散修正KdV-II方程；通过引入势变量，得到这两个方程的势形式，并证明其三维相容性.
关键词: 规范变换, 三维相容性, 离散KdV方程
Abstract: As to integrable partial differential equations, gauge transformations are important tools to extend integrable equations. In this letter, we investigate gauge transformations for discrete integrable equations. By applying twice gauge transformations to the Lax pair of the discrete Korteweg-de Vries (KdV) equation, we obtain discrete modified KdV and discrete modified KdV-II equations; by introducing the potential variables, we obtain potential forms of those two equations, which are proven to satisfy the three-dimensional consistency property.
Key words: gauge transformations, 3D consistency, lattice KdV equations
中图分类号:
O 29
张海菲, 张成, 张大军. 离散KdV方程的规范变换[J]. 上海大学学报(自然科学版), doi: 10.12066/j.issn.1007-2861.2268.
ZHANG Haifei, ZHANG Cheng, ZHANG Dajun. Gauge transformations for lattice KdV equations[J]. Journal of Shanghai University（Natural Science Edition）, doi: 10.12066/j.issn.1007-2861.2268.
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链接本文: https://www.journal.shu.edu.cn/CN/10.12066/j.issn.1007-2861.2268
