对可积偏微分方程的Lax对作规范变换是拓展可积方程的重要工具.本文主要研究可积离散方程的规范变换.通过对离散Korteweg-de Vries (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.
With respect to integrable partial differential equations, gauge transformations of Lax pairs are critical tools that can be used to extend integrable equations. 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. Then, by introducing the potential variables, we obtain potential forms of those two equations, which are proven to satisfy the three-dimensional consistency property.
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