通过具有两个导数的伪微分算子实现 KP-mKP 层次结构

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-07-31 DOI:10.1088/1361-6544/ad64a4

Lumin Geng, Jianxun Hu, Chao-Zhong Wu

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引用次数: 0

摘要

通过使用包含两个导数的伪微分算子，我们将卡多姆采夫-彼得维亚什维利（KP）层次结构扩展为某种 KP-mKP 层次结构。对于 KP-mKP 层次结构，我们推导出了它的 Bäcklund 变换、Baker-Akhiezer 函数的双线性方程和 tau 函数的 Hirota 方程。此外，我们还证明了该层次等价于与黎曼球相关的色散惠森层次的一个子层次，其无穷远点和一个可动点被标记。

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A KP-mKP hierarchy via pseudo-differential operators with two derivations

By using pseudo-differential operators containing two derivations, we extend the Kadomtsev–Petviashvili (KP) hierarchy to a certain KP-mKP hierarchy. For the KP-mKP hierarchy, we derive its Bäcklund transformations, bilinear equations of Baker–Akhiezer functions and Hirota equations of tau functions. Moreover, we show that this hierarchy is equivalent to a subhierarchy of the dispersive Whitham hierarchy associated to the Riemann sphere with its infinity point and one movable point marked.

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.