大分级修正的户田等级体系及其扩展

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2024-08-29 DOI:10.1016/j.physd.2024.134343

Yi Yang , Wenjuan Rui , Jipeng Cheng

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引用次数: 0

摘要

修正的户田层次结构只是双分量第一修正的KP层次结构，它通过三浦变换与二维户田层次结构相关，也被广泛用于讨论B-户田和C-户田层次结构。本文首先构造了（N,M）-大等级修正户田层次结构（BMTH）作为修正户田层次结构的还原，并给出了相应的李代数解释。然后，我们提出了 (N,M)-BMTH 的两种扩展。一种是使用对数流的扩展，另一种是 (2+1)D 扩展，它与环形李代数 slntor 相对应。最后，还讨论了这两种扩展的关系。

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Bigraded modified Toda hierarchy and its extensions

Modified Toda hierarchy is just the two-component first modified KP hierarchy, which is related to 2D Toda hierarchy through Miura transformation and also has been widely used in discussing the B-Toda and C-Toda hierarchies. In this paper, we firstly construct $(N, M)$ -bigraded modified Toda hierarchy (BMTH) as a reduction of modified Toda hierarchy, and give corresponding Lie algebra interpretation. After that, we propose two kinds of extensions of $(N, M)$ -BMTH. One is extended by using logarithmic flows, while the other is $(2 + 1)$ D extension, which is corresponding to the toroidal Lie algebra ${sl}_{n}^{tor}$ . At last, the relation of these two kinds of extensions also is discussed.

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.