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INdAM Fellowship Programs in Mathematics and/or Applications cofunded by Marie Skłodowska-Curie Actions



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Federico Zullo

 

INdAM-COFUND Outgoing fellow between 2012-01-10 and 2014-01-09

Project information

Title

BTceq: Backlund Transformations for Classical and Quantum Integrable Systems

Outgoing host organisation                           Return host organisation

University of Kent                                                      Università degli Studi Roma Tre

Cornwallis Building                                                   Via della Vasca Navale 84
CT2 7NF Canterbury, United Kingdom                 00146 Roma, Italy

http://www.kent.ac.uk/                                           http://www.fis.uniroma3.it/

Abstract

The research project is conceived on the potential applications and properties of the theory of Bäcklund transformations to non-linear evolution equations, in particular to finite-dimensional integrable systems, both quantum and classical. This line of research covers a broad spectrum of aspects related to integrable discretizations and exact-time discretizations, separation of variables and factorization of eigenfunctions.

For the classical case the main goal would be to enlighten the interplay between the Bäcklund transformations theory and the classical results of Hamiltonian mechanics and separation of variables, elucidating the role that these transformations could play as a tool to obtain exact time-discretization of the underlying continuous integrable classical model; here the adjective exact means the identity among the discrete trajectories described by the map defined by the transformations and the continuous trajectories defined by the integrable model.

A second aspect would be to clarify to what extent the above constructions can be, mutatis mutandis, transferred to the infinite dimensional case, i.e. to Bäcklund transformations for partial differential or differential-difference equations.

These findings could give then the possibility to better understand the noticed connections among the Baxter Q-operator, the Baxter equation and quantum Bäcklund transformations. The link with the classical case is represented by the integral kernel of the Q-operator, which in the semi-classical limit is exactly the generating function of the canonical transformations defined by the Bäcklund transformations.

Year 1 Report

The report on the first year of the project can be downloaded from this link

Fellow information

Research interests

Current research interests are twofold:

  • Bäcklund Transformations Theory, Hamiltonian and
    Dissipative Non-Linear Evolution Equations, Soliton Theory, Integrable
    Systems, their geometric and algebraic properties and their integrable
    discretizations.
  • Ecological modelling, population dynamics and
    sustainable development, in particular with application to the concept
    of “exergy”

Previous positions, awards

  • January 2011: Phd in Mathematical Physics at the Doctoral School in Mathematics and Physics, Physics Department of Roma TRE University
  • September 2005: MSc (Laurea Magistrale) in Physics cum Laude, Università “Roma Tre”
  • 2005: awarded with Premio Galluzzi per la fisica 2005 (academic prize for high achievements in graduate studies)
  • July 2003: BSc (Laurea) in Physics cum Laude, Università “Roma Tre”

Publications, preprints, other works

  1. O. Ragnisco, F. Zullo, Continuous and Discrete (Classical) Heisenberg Spin Chain revised, SIGMA (Symmetry, Integrability and Geometry:
    Methods and Applications) 3 (2007), 033
  2. O. Ragnisco, F. Zullo, Bäcklund Transformations for the Trigonometric
    Gaudin Magnet: first results
    , SIGMA (Symmetry, Integrability and Geometry:
    Methods and Applications) 6 (2010), 012, 6 pages
  3. E. Sciubba, F. Zullo, Exergy based population dynamics: a thermodynamic
    view of the sustainability concept
    , 2011. Journal of Industrial Ecology, 15, Issue 2,
    pp. 172–184, April 2011
  4. E. Sciubba, F. Zullo, Is Sustainability a Thermodynamic concept?, International Journal of Exergy 2011 – 8, No.1
     pp. 68 – 85
  5. O. Ragnisco, F. Zullo, Bäcklund transformations as exact integrable
    time-discretizations for the trigonometric Gaudin model
    , Journal of Physics A: Mathematical and
    Theoretical. 43, 434029, 2010
  6. O. Ragnisco, F. Zullo, Bäcklund Transformation for the Kirchhoff Top, SIGMA (Symmetry, Integrability and Geometry:
    Methods and Applications), 7 (2011), 001, 13 pages
  7. F. Zullo, Bäcklund Transformation for the elliptic Gaudin
    model and a Clebsch system
    , J. Math. Phys. 52, 073507 (2011)
  8. O. Ragnisco, F. Zullo, Quantum Bäcklund Transformation: some ideas and examples, contribution to Solitons in 1+1 and 2+1
    dimensions, DS, KP and all that, conference in honor of the 70th
    birthday of Marco Boiti and Flora Pempinelli. Lecce, 2011 September
    13-14. To appear in Theoretical and Mathematical Physics
  9. E. Sciubba, F. Zullo, Stability and limit cycles in an exergy-based
    model of population dynamics
    , contribution to Proceedings of ECOS 2012, 25th
    International Conference on Efficiency, Cost, Optimization, Simulation
    and Environmental Impact of Energy Systems June 26-29, 2012, Perugia,
    Italy

Conferences, schools, other events

  • Workshop Nonlinear Waves and Integrable Systems
    Roma Tre University, Department of Physics, Roma,
    Italy, February 2009
  • Ravello Summer School in Mathematical Physics,
    XXXIV edition

    Ravello, Italy, September 2009
  • Trasformazioni di Bäcklund per il modello
    trigonometrico di Gaudin (Bäcklund Transformations for the
    trigonometric Gaudin model)

    Talk delivered at Assemblea Scientifica G.N.F.M.
    Montecatini Terme, Italy, October 2009
  • Plenary talk “An exact time discretization
    for the Kirchhoff top via Bäcklund transformation for the
    trigonometric Gaudin Model”

    at XIXth International Colloquium on
    Integrable Systems and Quantum Symmetries

    Prague, Czech Republic, June 2010
  • London Mathematical Society and EPSRC Short
    Instructional Course on Classical & Quantum Integrable Models

    Canterbury, University of Kent, United Kingdom, July 2010
  • Bäcklund transformations for the elliptic Gaudin
    magnet

    Talk delivered at Department of Mathematics and Applications,
    University of Milano-Bicocca

    Milano, Italy, October 2010
  • Bäcklund transformation and time-discretizations
    for the elliptic Gaudin Model

    workshop Discrete Integrable Systems
    Lorentz Center, Leiden, Holland, 18-22 July 2011
  • Separation of variables, Bäcklund transformations
    and “spectrality property” for finite dimensional integrable
    systems

    conference Finite Dimensional Integrable
    Systems in Geometry and Mathematical Physics

    Jena, Germany, 26-29 July 2011
  • Exact time discretisations via Bäcklund
    transformations: general ideas and examples

    Talk delivered at Bi-Hamiltonian Systems and All That, Conference in
    honour of Franco Magri’s 65th birthday

    Dipartimento di Matematica e Applicazioni,
    Università di Milano-Bicocca & Dipartimento di Ingegneria
    dell’Informazione e Metodi Matematici, Università di Bergamo, 27 September-1 October 2011
  • Invited talk “Exergy-driven population
    dynamics”

    at Dipartimento di Ingegneria Elettronica,
    Dipartimento di Fisica & INFN – Sezione di Roma Tre, Roma Tre
    University

    Roma, Italy, 15 December 2011
  • British Mathematical Colloquium & Mathematical
    Physical Workshop

    University of Kent, Canterbury, Kent, 16-19 April 2012
  • Euroscience Open Forum & Marie Curie Actions
    Conference

    Dublin, Ireland, 10-15 July 2012
  • Invited instructor at Summer School of
    Thermodynamics

    Anzio, Italy, 11-23 June 2012
  • Assemblea Scientifica GNFM 2012
    Montecatini Terme, Italy, 4-6 October 2012

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