Integrability, Integrable Systems, and Their Applications

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

Deadline for manuscript submissions: closed (30 September 2019)

Special Issue Editor


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Guest Editor
School of Mathematical and Statistical Science, The University of Texas Rio Grande Valley, Edinberg, TX 78540, USA
Interests: mathematical physics; differential geometry; functional analysis
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Special Issue Information

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

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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

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

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Published Papers

There is no accepted submissions to this special issue at this moment.
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