Integrability, Integrable Systems, and Their Applications

Dear Colleagues,

This is to announce a Special Issue dedicated to the topic of Integrable Systems. Originally, an integrable system is a system of differential equations whose behavior is determined by its initial conditions and which can be integrated from those initial conditions.

Many systems of differential equations in physics are integrable. A standard example is the motion of a rigid body about its center of mass. This system gives rise to a number of conserved quantities, the angular momenta. Conserved quantities such as these are known as the first integrals of the system.

Roughly speaking, if there are enough first integrals to give a coordinate system on the set of solutions, then it is possible to reduce the original system of differential equations to an equation that can be solved by computing an explicit integral. Other models in physics giving rise to integrable systems in physics are the KdV equation for shallow water waves, the nonlinear Schrodinger equation, and the Toda lattice in statistical mechanics. Hitchin mentions three generally recognizable features of integrable systems: The existence of many conserved quantities; the presence of algebraic geometry; and the ability to give explicit solutions.

Papers will be considered on any relevant topic that falls under the scope of the title, as well as:

• Frobenius integrability and overdetermined differential systems;
• General dynamical systems;
• Hamiltonian systems and Liouville integrability;
• The Hamilton-Jacobi approach;
• Solitons and Inverse spectral methods;

We especially seek papers on quantum integrable systems, as these have played a major role. Finally, we invited papers on exactly solvable models.

Prof. Dr. Paul Bracken
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.

• Quantum integrable
• Solitons and differential geometry
• Solvable
• Action–angle variables
• Inverse scattering transform