Matteo Sommacal's main scientific interests
span over many topics in the field of Mathematical-Physics and can
be essentially collected in 7 main research lines, each of them
corresponding to several fruitful, long-standing and
well-established scientific collaborations.
 Isochronicity and the transition from ordered to disordered
motions for dynamical systems
Short Description: Study and classification of integrable and
non-integrable many-body problems featuring periodic solutions.
Applications to periodic (isochronous) natural phenomena (e.g.
periodic chemical reactions). Study of the transitions from ordered
to disordered motions for dynamical systems, explained as travels on
Riemann surfaces. Analysis of the mechanisms for the onset of
irregular (chaotic) motions in a deterministic context and
definition of an alternative route to explaining chaotic motions via
the analytic structure (branching) of the solutions in the complex
Keywords: integrable and super-integrable systems; dynamical
systems; Hamiltonian systems; isochronicity; singularities in
complex time; transitions to chaos; Lyapunov exponents; PainlevÚ and
poly-PainlevÚ analysis; Psi-series; Riemann surfaces; complex
analysis; monodromy group; Fuchsian equations; continued fractions;
numerical integration of ordinary differential equations; periodic
Collaborations: Francesco Calogero and Paolo Maria Santini,
UniversitÓ degli Studi di Roma "La Sapienza" (Italy) and David
Gomez-Ullate, Universidad Complutense de Madrid (Spain); other
results where obtained in collaboration with Jean-Pierre Franšoise,
UniversitÚ P. et M. Curie, Paris VI, Paris (France); Andrew Hone,
University of Kent (UK); Franšois Leyvraz, Universidad de los Andes,
BogotÓ (Columbia); Piotr Grinevich, Landau Institut, Moscow
Period: 2002 - Present days.
 Continuous elastic rods as models for polymeric chains and
Short Description: Analytical and numerical study of the
dynamical Kirchhoff equations for an elastic rod (a system of nine
coupled nonlinear PDEs in 1+1 dimensions) as a model for polymeric
chains and protein folding. Full classification of all the circular
helical (stable and unstable) con gurations for the static problem.
Analysis of the time evolution of a strainable rod.
Keywords: continuous media; isotropic and anisotropic
elasticity; Cosserat continuum; De Saint Venant's theory of beams;
coarse-grained structures; mechanical properties and constitutive
equations of a thin elastic rod; Young and shear moduli; Kirchhoff
equations; numerical integration of systems of PDEs; perturbative
and asymptotic analysis; alpha helices and beta sheets; polymeric
chains; protein folding.
Collaborations: Mark J. Ablowitz, Colorado University at
Boulder (CO, USA); Vincenzo Barone, Scuola Normale
Superiore di Pisa (Italy); Mario Argeri, UniversitÓ degli Studi di
Napoli Federico II (Italy); Silvana De Lillo and Gaia Lupo,
UniversitÓ di Perugia (Italy).
Period: 2007 - Present days.
 Moving magnetic droplet solitons
Short Description: Landau-Lifshitz equation in two spatial
dimensions as a model for spin-wave excitation using a point contact
in a thin ferromagnetic film.
Keywords: Landau-Lifshitz equation; spin-wave excitation;
localized solutions; numerical integration of PDEs.
Collaborations: Mark Hoefer, North Carolina State University,
Raleigh (NC, USA).
Period: 2009 - Present days.
 The onset and the interaction of dispersive and dissipative
Short Description: Study of the onset and of the interaction
of dispersive and dissipative shock waves as solutions of integrable
and nonintegrable nonlinear evolution equations, starting from
Kamchatnov theory on the approximation of Whitham modulation
equations to describe oscillatory solutions in dispersive means.
Keywords: inverse scattering transform; shock waves; Whitham
equations; elliptic integrals; perturbative and asymptotic analysis;
Burgers equation; KdV equation; NLS equation; KdV-Burgers equation;
Bose-Einstein condensates; numerical integration of PDEs.
Collaborations: Silvana De Lillo and Gaia Lupo, UniversitÓ
degli Studi di Perugia (Italy); Mark J. Ablowitz, Colorado
University at Boulder (CO, USA); Mark Hoefer, North Carolina State
University, Raleigh (NC, USA).
Period: 2007 - Present days.
 Evolutionary integrable models in multidimension
Short Description: Formulation of new solvable nonlinear (systems
of) evolution PDEs in multidimensional space, involving rational,
trigonometric and elliptic functions of the independent variables.
Keywords: nonlinear evolution PDEs in multidimensions;
solvable PDEs; NLS-like equations; nonlinear Klein-Gordon-like
equations; elliptic functions; isochronicity; numerical integration
Collaborations: Francesco Calogero, UniversitÓ degli Studi di
Roma "La Sapienza" (Italy) and Jean-Pierre Franšoise, UniversitÚ P.
et M. Curie, Paris VI, Paris (France).
Period: 2006 - 2007.
 Initial conditions/boundary value problems
Short description: (1) Nonlinear heat conduction problems for
Storm materials. (2) The Neumann problem on the semi-line for the
Burgers equation. (3) A nonlinear model of sulphation phenomena in
calcium carbonate stones. Keywords: Dirichlet, Neumann and Robin
problems; moving boundaries; Hopf-Cole transformation; hodographic
transformations; numerical integration of PDEs.
Collaborations: Silvana De Lillo and Gaia Lupo, UniversitÓ di
Period: 2006 - 2007.
 Combinatoric and geometrical methods for Archaeology
Short Description: (1) Development and numerical
implementation of seriation techniques to derive the relative
chronology of archaeological data. (2) Polynomial interpolation
techinques (cubic spline) to define cultural and political
boundaries from topographic archaeological data.
Keywords:relative chronologies; Ihm algorithm; the traveling
salesman's problem; optimization problems; Voronoi diagrams;
Hamiltonian paths; labeled graphs; cubic splines.
Collaborations: European Proto-History Chair, Paola Piana
Agostinetti, UniversitÓ degli Studi "La Sapienza", Roma (Italy).
Period: 2004 - Present days.