[Formula: see text] graded discrete Lax pairs and Yang-Baxter maps.
[Formula: see text] graded discrete Lax pairs and Yang-Baxter maps.
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【公式：见正文】分级离散Lax对和Yang-Baxter图。
DOI：
10.1098/rspa.2016.0946
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Fordy AP
中科院分区：
文献类型：
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作者：
Fordy AP
最近，我们引入了一类分次离散Lax对，并研究了相应的离散可积系统（格方程）.本文引入了相应的Yang-Baxter映射。当N =2时，许多著名的例子都属于这个方案，因此，当N ≥3时，我们的系统可以看作是这些方案的推广。特别地，对于每个N，我们引入一类多分量Yang-Baxter映射，其包括HB III（Papageorgiouet al.2010SIGMA6，003（9 p）. (doi：10.3842/SIGMA.2010.033）），当N =2时，以及当N =3时，与离散修正Boussinesq方程相关联的。对于N ≥5，我们引入了一族新的Yang-Baxter映射，它没有低维类似物.我们还提出了新的多分量版本的杨巴克斯特地图FIV和FV（在Adleret等人的分类。Anal. Geom.12，967-1007。(doi：10.4310/CAG.2004.v12.n5.a1））。
We recently introduced a class ofgraded discrete Lax pairs and studied the associated discrete integrable systems (lattice equations). In this paper, we introduce the corresponding Yang–Baxter maps. Many well-known examples belong to this scheme forN=2, so, forN≥3, our systems may be regarded as generalizations of these. In particular, for eachNwe introduce a class of multi-component Yang–Baxter maps, which includeHBIII(of Papageorgiouet al.2010SIGMA6, 003 (9 p). (doi:10.3842/SIGMA.2010.033)), whenN=2, and that associated with the discrete modified Boussinesq equation, forN=3. ForN≥5 we introduce a new family of Yang–Baxter maps, which have no lower dimensional analogue. We also present new multi-component versions of the Yang–Baxter mapsFIVandFV(given in the classification of Adleret al.2004Commun. Anal. Geom.12, 967–1007. (doi:10.4310/CAG.2004.v12.n5.a1)).