

Francesco CALOGERO
Professor 
Born: 6 February 1935, Fiesole, Italy
Education:
 February 1958, graduated ["laurea in fisica"] cum laude in Rome
Current Professional Status:
Membership:
Honours:
Areas of Expertise:
 integrable nonlinear evolution partial differential equations,
 solvable dynamical systems,
 scattering theory,
 quantum field theory, nuclear manybody problem,
 special functions,
 finitedimensional representations of operators,
numerical computation of the eigenvalues of differential operators
Author:
 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):
 F. Calogero, Variable phase approach to potential scattering, Academic
Press, New York, 1967 (translated into Russian in 1972).
 F. Calogero and A. Degasperis, Spectral transform and solitons, North
Holland, Amsterdam, 1982 (translated into Russian in 1985).
 F. Calogero,
Classical manybody problems amenable to exact treatments
(Lecture Notes in Physics Monograph m66), Springer, 2001.
Some Results on Integrable Systems:
 introduction and solution of the quantum
onedimensional manybody problem with inverse square twobody potentials;
 discovery via the Lax technique of the integrability of a class of classical
manybody problems (first introduction of elliptic interactions in manybody
integrable models; first introduction of functional equations in this
field);
 introduction of a new technique to identify integrable
onedimensional manybody problems, with many examples (later extended to
rotationinvariant twobody 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 manybody problems in ordinary
(threedimensional) space, with several new examples characterized by
rotationinvariant 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 phasedspace 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
I00185 ROMA (Italy)
Emails:
francesco.calogero@roma1.infn.it,
calogero@uniroma1.it
Home page:
http://www.phys.uniroma1.it/DOCS/TEO/people/calogero.txt


