Advanced Research in Mathematical Physics Models with Painlevé Property and Affine Weyl Group Symmetry

Dear Colleagues,

We are pleased to announce a call for papers for a Special Issue dedicated to advanced research in mathematical physics models with the Painlevé property and affine Weyl group symmetry. Infinite-dimensional Lie algebras play a key role in many developments in integrable models that give rise to Painlevé equations in their self-similarity limits. These equations are invariant under symmetry groups of the Bäcklund transformations that form the affine Weyl groups. This connection relates the Painlevé property to the concept of integrability for non-linear differential equations.

This Special Issue seeks to exploit a link between infinite-dimensional Lie algebras and integrable systems and affine Weyl groups and Painlevé equations to form a unifying perspective that binds together a wide array of the latest developments on a wide variety of topics that include, but are not limited to:

• A remarkable connection between Painlevé equations and a wide range of problems of mathematical physics, random matrix theory, etc., where Painlevé equations find active applications.
• Novel descriptions of solutions of Painlevé equations, including rational solutions, the classical special functions such as hypergeometric-type solutions, transcendental functions and Umemura polynomials aided by various algebraic and group theoretical methods and techniques.
• Discrete Painlevé equations and their relations to the symmetry structure of Painlevé equations and orthogonal polynomials.
• Studies of the symmetry structure of Painlevé equations and their generalizations in terms of root systems associated with affine Weyl groups and their applications to solutions, including study of zeros and poles of rational solutions.
• Origins of Painlevé equations as self-similarity limits of integrable models as studied by Lax, Hamiltonian and zero curvature approaches. Connection to various integrable models, e.g., Calogero–Moser models, Toda models, Volterra models and dressing chain equations.

We invite original research articles, review articles and short communications that address the above topics or related areas. All manuscripts will be subject to a rigorous peer review process, and accepted papers will be published in this Special Issue of the journal. We welcome submissions from researchers in mathematics, physics and related fields who are active in the study of integrable models and Painlevé equations in mathematical physics settings and interested in advances achieved through applications of symmetry considerations.

We look forward to your participation and contributions to this Special Issue. 

Prof. Dr. Henrik Aratyn
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.

• mathematical Physics
• integrable models
• Painlevé equations
• applications of symmetry