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Francesco Calogero   

Francesco CALOGERO


Born: 6 February 1935, Fiesole, Italy


  • February 1958, graduated ["laurea in fisica"] cum laude in Rome

Current Professional Status:



Areas of Expertise:

  • integrable nonlinear evolution partial differential equations,
  • solvable dynamical systems,
  • scattering theory,
  • quantum field theory, nuclear many-body problem,
  • special functions,
  • finite-dimensional representations of operators, numerical computation of the eigenvalues of differential operators


  • scientific publications (in English): 3 books and over 300 papers;
  • publications on science and society: several books and about 390 papers (half in English)

Main Scientific Publications (Books):

Some Results on Integrable Systems:

  • introduction and solution of the quantum one-dimensional many-body problem with inverse square two-body potentials;
  • discovery via the Lax technique of the integrability of a class of classical many-body problems (first introduction of elliptic interactions in many-body integrable models; first introduction of functional equations in this field);
  • introduction of a new technique to identify integrable one-dimensional many-body problems, with many examples (later extended to rotation-invariant two-body problems);
  • introduction of a new general technique to identify and investigate integrable nonlinear PDEs;
  • spectral interpretation of Bäcklund transformations;
  • identification of several new integrable nonlinear PDEs (with A. Degasperis);
  • elaboration of the multiscale reduction technique (in the form introduced by W. Eckhaus) and introduction of the notion of "universal" equations, which are therefore both integrable and widely applicable;
  • introduction of a technique to discover integrable many-body problems in ordinary (three-dimensional) space, with several new examples characterized by rotation-invariant Newtonian equations of motion (with M. Bruschi);
  • introduction of the notion of "nonlinear harmonic oscillator", with interesting examples (with V. Inozemtsev);
  • investigation of "isochronous systems" (system that possess an open region having full dimensionality in their phase space where all solutions are completely periodic with a fixed period), with the observation that "such systems are not rare" (indeed, almost any dynamical system can be deformed so that the deformed system is isochronous);
  • investigation of the behavior of certain isochronous systems outside of their phased-space region of isochronicity, and of a mechanism to explain (as travel over Riemann surfaces) the transition from ordered to disordered motions, including the onset of a new kind of deterministic chaos.

Mailing Address:
Department of Physics
University of Rome "La Sapienza"
p. Aldo Moro
I-00185 ROMA (Italy)

E-mails: francesco.calogero@roma1.infn.it, calogero@uniroma1.it
Home page: http://www.phys.uniroma1.it/DOCS/TEO/people/calogero.txt

Page last updated: 14 April 2005 Main page of the EqWorld website


Classical many-body problems amenable to exact treatments

Spectral transform and solitons [in Russian]. Moscow: Mir, 1985

Variable phase approach to potential scattering [in Russian]. Moscow: Mir, 1972