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Symmetry
Special Issues
Symmetry and Integrable System
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Symmetry and Integrable System

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 January 2023) | Viewed by 3966

Special Issue Editor

Prof. Dr. Yufeng Zhang

E-Mail Website
Guest Editor
School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
Interests: ordinary differential equations; partial differential equations; soliton theory; integrable systems
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Soliton theory and integrable systems are important aspects of mathematical physics. Subtopics include soliton solutions, symmetry analysis, Darboux transformation, Hamiltonian structure, and so on.

Darboux transformation of integrable equations is an important tool for searching for soliton solutions through spectral problems or Lax pairs. Symmetry obtained by the Lie group of transformations is important in the unusual properties of ordinary differential equations and partial differential equations, which has extensive applications in physics science.

The purpose of this issue is to demonstrate soliton solutions, Darboux transformations, symmetry of differential equations and Hamiltonian structure, and so on.

Submit your paper and select the Journal “Symmetry” and the Special Issue “Symmetry and Integrable System” via: MDPI submission system. Our papers will be published on a rolling basis and we will be pleased to receive your submission once you have finished it.

Prof. Dr. Yufeng Zhang
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. Symmetry is an international peer-reviewed open access monthly 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 2400 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

  • soliton solution
  • symmetry
  • Darboux transformation
  • Hamiltonian structure
  • integrable system

Published Papers (3 papers)

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Research

10 pages, 270 KiB  
Article
Inequalities for q-h-Integrals via ℏ-Convex and m-Convex Functions
by Dong Chen, Matloob Anwar, Ghulam Farid and Waseela Bibi
Symmetry 2023, 15(3), 666; https://0-doi-org.brum.beds.ac.uk/10.3390/sym15030666 - 07 Mar 2023
Cited by 5 | Viewed by 993
Abstract
This paper investigates several integral inequalities held simultaneously for q and h-integrals in implicit form. These inequalities are established for symmetric functions using certain types of convex functions. Under certain conditions, Hadamard-type inequalities are deducible for q-integrals. All the results are [...] Read more.
This paper investigates several integral inequalities held simultaneously for q and h-integrals in implicit form. These inequalities are established for symmetric functions using certain types of convex functions. Under certain conditions, Hadamard-type inequalities are deducible for q-integrals. All the results are applicable for ℏ-convex, m-convex and convex functions defined on the non-negative part of the real line. Full article
(This article belongs to the Special Issue Symmetry and Integrable System)
19 pages, 574 KiB  
Article
Integrable Coupling of Expanded Isospectral and Non-Isospectral Dirac Hierarchy and Its Reduction
by Cheng Chen, Jian Zhou, Shiyin Zhao and Binlu Feng
Symmetry 2022, 14(12), 2489; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14122489 - 24 Nov 2022
Cited by 2 | Viewed by 796
Abstract
In this paper, we first generalize the Dirac spectral problem to isospectral and non-isospectral problems and use the Tu scheme to derive the hierarchy of some new soliton evolution equations. Then, integrable coupling is obtained by solving the isospectral and non-isospectral zero curvature [...] Read more.
In this paper, we first generalize the Dirac spectral problem to isospectral and non-isospectral problems and use the Tu scheme to derive the hierarchy of some new soliton evolution equations. Then, integrable coupling is obtained by solving the isospectral and non-isospectral zero curvature equations.We find that the obtained hierarchy has the bi-Hamiltonian structure of the combined form. In particular, one of the integrable soliton hierarchies is reduced to be similar to the coupled nonlinear Schördinger system in the AKNS hierarchy. Next, the strict self-adjointness of the reduced equation system is verified, and conservation laws are constructed with the aid of the Ibragimov method. In addition, we apply the extended Kudryashov method to obtain some exact solutions of this reduced equation system. Full article
(This article belongs to the Special Issue Symmetry and Integrable System)
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9 pages, 249 KiB  
Article
Lie Symmetry Analysis, Particular Solutions and Conservation Laws of Benjiamin Ono Equation
by Zhenli Wang, Liangji Sun, Rui Hua, Lihua Zhang and Haifeng Wang
Symmetry 2022, 14(7), 1315; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14071315 - 25 Jun 2022
Cited by 3 | Viewed by 1204
Abstract
In this paper, by applying the Lie group method and the direct symmetry method, Lie algebras of the Benjiamin Ono equation are obtained, and we find that results of the two methods are same. Based on the Lie algebra, Lie symmetry groups, relationships [...] Read more.
In this paper, by applying the Lie group method and the direct symmetry method, Lie algebras of the Benjiamin Ono equation are obtained, and we find that results of the two methods are same. Based on the Lie algebra, Lie symmetry groups, relationships between new solutions and old solutions, two kinds of ODEs as symmetry reductions are obtained. Making use of the power series method, the exact power series solution of the Benjiamin Ono equation has been derived. We also give the conservation laws of Benjiamin Ono equation by means of Ibragimovs new conservation Theorem. Full article
(This article belongs to the Special Issue Symmetry and Integrable System)
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