论格网方程的轨距等价关系下的拉克斯表征和米乌拉型变换

arXiv - PHYS - Exactly Solvable and Integrable Systems Pub Date : 2024-05-14 DOI:arxiv-2405.08579

Sergei Igonin

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引用次数: 0

摘要

我们研究微分-差分（网格）方程的矩阵拉克斯表示（MLR）。对于一个给定方程，如果两个 MLR 中的一个可以通过矩阵量规变换从另一个得到，那么这两个 MLR 可以说是量规等价的。我们将介绍有关以下问题的结果：1.给定的 MLR 何时与适合通过[G.Berkeley, S. Igonin, J. Phys. A (2016), arXiv:1512.09123] 方法构造微分差分米乌拉型变换的 MLR 轨距等价？2.给定的 MLR 量规何时等价于微不足道的 MLR？此外，我们还提出了具有米乌拉型变换的可积分微分-差分方程的新例子。

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On Lax representations under the gauge equivalence relation and Miura-type transformations for lattice equations

We study matrix Lax representations (MLRs) for differential-difference (lattice) equations. For a given equation, two MLRs are said to be gauge equivalent if one of them can be obtained from the other by means of a matrix gauge transformation. We present results on the following questions: 1. When is a given MLR gauge equivalent to an MLR suitable for constructing differential-difference Miura-type transformations by the method of [G. Berkeley, S. Igonin, J. Phys. A (2016), arXiv:1512.09123]? 2. When is a given MLR gauge equivalent to a trivial MLR? Furthermore, we present new examples of integrable differential-difference equations with Miura-type transformations.

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arXiv - PHYS - Exactly Solvable and Integrable Systems

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