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Mathematics
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Symmetries of Integrable Systems
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Symmetries of Integrable Systems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (20 July 2023) | Viewed by 1993

Special Issue Editor

Prof. Dr. Chuanzhong Li

E-Mail Website
Guest Editor
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
Interests: mathematical physics; algebra nonlinear systems; differential equations

Special Issue Information

Dear Colleagues, 

The symmetries of integrable systems are important in studies on integrable systems, including the Virasoro symmetries. In these symmetries, the additional symmetry is an interesting and important one. As we know, the Kadomtsev–Petviashvili (KP) hierarchy is an important integrable system that attracts more and more attention in mathematical physics. Additional symmetries of the KP hierarchy were introduced by Orlov and Shulman that contain Virasoro symmetries, which have Virasoro constraints on partition functions of matrix models of string theory under the additional non-isospectral symmetries. There are two important sub-hierarchies of the KP hierarchy, which are the BKP hierarchy and the CKP hierarchy. Similar cases can be used in the Toda hierarchy. We welcome authors to submit their papers to our Special Issue. 

Prof. Dr. Chuanzhong Li
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • KP hierarchy
  • toda hierarchy
  • symmetry

Published Papers (2 papers)

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Research

8 pages, 250 KiB  
Article
Similarity Transformations and Nonlocal Reduced Integrable Nonlinear Schrödinger Type Equations
by Li Cheng and Wen-Xiu Ma
Mathematics 2023, 11(19), 4110; https://0-doi-org.brum.beds.ac.uk/10.3390/math11194110 - 28 Sep 2023
Cited by 4 | Viewed by 666
Abstract
We present three reduced integrable hierarchies of nonlocal integrable nonlinear Schrödinger-type equations, starting from a given vector integrable hierarchy generated from a matrix Lie algebra of B type. The basic tool is the zero curvature formulation. Three similarity transformations are taken to keep [...] Read more.
We present three reduced integrable hierarchies of nonlocal integrable nonlinear Schrödinger-type equations, starting from a given vector integrable hierarchy generated from a matrix Lie algebra of B type. The basic tool is the zero curvature formulation. Three similarity transformations are taken to keep the invariance of the involved zero curvature equations. The key is to formulate a matrix solution to a reduced stationary zero curvature equation such that the zero curvature formulation works for a reduced case. Full article
(This article belongs to the Special Issue Symmetries of Integrable Systems)
9 pages, 255 KiB  
Article
Higher-Order Matrix Spectral Problems and Their Integrable Hamiltonian Hierarchies
by Shou-Ting Chen and Wen-Xiu Ma
Mathematics 2023, 11(8), 1794; https://0-doi-org.brum.beds.ac.uk/10.3390/math11081794 - 10 Apr 2023
Viewed by 962
Abstract
Starting from a kind of higher-order matrix spectral problems, we generate integrable Hamiltonian hierarchies through the zero-curvature formulation. To guarantee the Liouville integrability of the obtained hierarchies, the trace identity is used to establish their Hamiltonian structures. Illuminating examples of coupled nonlinear Schrödinger [...] Read more.
Starting from a kind of higher-order matrix spectral problems, we generate integrable Hamiltonian hierarchies through the zero-curvature formulation. To guarantee the Liouville integrability of the obtained hierarchies, the trace identity is used to establish their Hamiltonian structures. Illuminating examples of coupled nonlinear Schrödinger equations and coupled modified Korteweg–de Vries equations are worked out. Full article
(This article belongs to the Special Issue Symmetries of Integrable Systems)
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