论 Dubrovin-Frobenius 流形的 B 型族及其可积分系统

IF 1.3 3区物理与天体物理 Q3 PHYSICS, MATHEMATICAL Letters in Mathematical Physics Pub Date : 2024-10-13 DOI:10.1007/s11005-024-01867-z

Alexey Basalaev

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引用次数: 0

摘要

根据左小祖咒和贝尔托拉（Bertola）的一项未发表的研究，存在一个与 B 型考克赛特群相关的杜布罗文-弗罗贝纽斯流形结构的双指数系列。我们研究了不同指数值下这些结构之间的关系。我们证明，这种以 (k, l) 为索引的 Dubrovin-Frobenius 流形的部分数据可以通过（(k+r,l+r)）恢复。继续巴萨拉耶夫等人（J Phys A: Math Theor 54:115201，2021）的计划，我们将一个无穷换向 PDEs 系统与这些 Dubrovin-Frobenius 流形联系起来，并证明这些 PDEs 扩展了无色散 BKP 层次。

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On B-type family of Dubrovin–Frobenius manifolds and their integrable systems

According to Zuo and an unpublished work of Bertola, there is a two-index series of Dubrovin–Frobenius manifold structures associated to a B-type Coxeter group. We study the relations between these structures for the different values of these indices. We show that part of the data of such Dubrovin–Frobenius manifold indexed by (k, l) can be recovered by the \((k+r,l+r)\) Dubrovin–Frobenius manifold.Continuing the program of Basalaev et al. (J Phys A: Math Theor 54:115201, 2021) we associate an infinite system of commuting PDEs to these Dubrovin–Frobenius manifolds and show that these PDEs extend the dispersionless BKP hierarchy.

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来源期刊

Letters in Mathematical Physics 物理-物理：数学物理

CiteScore

2.40

自引率

8.30%

发文量

111

审稿时长

3 months

期刊介绍： The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.