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Publications
- Book (PhD Thesis):
- Submitted papers:
- F. Demontis, G. Ortenzi, C. van der Mee: Inverse scattering transform for the Pohlmeyer-Lund-Regge equation
and reflectionless potential solutions
- F. Demontis, S. Lombardo, M. Sommacal, C. van der Mee, and F. Vargiu: Closed-form Soliton Solutions of the Continuous
Classical Heisenberg Ferromagnet Equation
- Journal articles:
- F. Borghero, F. Demontis: A 3-Dimensional Inverse Problem of Geometrical
Optics: a Mathematical Comparison Between Fermat's Principle and the Eikonal Equation. Journal of the Optical Society of America. A, Optics, Image Science, and Vision, 33 (9), 1710--1722, (2016), DOI: 10.1364/JOSAA.33.001710.
- F. Demontis, F. Vargiu, and C. van der Mee: Nonsmooth Spin Densities
for Continuous Heisenberg Spin Chains. Ricerche di Matematica, 65(2), 469--478 DOI:10.1007/s11587-016-0268-x, (2016).
- F. Demontis, G. Ortenzi, C. van der Mee:
Exact Solutions of the Hirota Equation and Vortex Filaments Motion .
Physica D 313 (2015), 61-80
- F. Demontis, B. Prinari, C. van der Mee and F. Vitale,
The inverse scattering transform for the focusing nonlinear
Schrödinger equation with asymmetric boundary conditions.
Journal of Mathematical Physics; 55 101505 (2014); doi: 10.1063/1.489876 (online first)
- F. Demontis and C. van der Mee,
Characterization of Scattering Data
for the Matrix Zakharov-Shabat System. Acta Appl Math (2014); 131 :29--47
DOI 10.1007/ s10440-013-9848-x
- F. Borghero, F. Demontis and S. Pennisi,
Wave Speeds in the Macroscopic Extended Model for Ultrarelativistic Gases.
J. Math. Phys. 54, 113101 (2013); doi: 10.1063/1.4829365
- F. Demontis and C. van der Mee,
An Alternative Approach to Integrable Discrete Nonlinear
Schrödinger Equations.
Acta Applicandae Mathematicae 127, 169-191 (2013). doi: 10.1007/s10440-012-9797-9
- F. Demontis, B. Prinari, C. van der Mee, and F. Vitale,
The inverse scattering transform for the defocusing nonlinear
Schrödinger equation with nonzero boundary conditions.
Studies in Applied Mathematics, Studies in Applied Mathematics 131(1), 1-40 (2013). doi:10.1111/j.1467-9590.2012.00572.x
- F. Borghero, F. Demontis, and S. Pennisi,
On the Hyperbolicity of a Model with 30 Moments for Ultrarelativistic Gases.
Meccanica, online version: 2012, DOI: 10.1007/s11012-012-9617-3 ( printed version:
48(3): 585-600 (2013))
- F. Demontis and C. van der Mee,
Closed Form Solutions to the integrable discrete nonlinear Schrödinger equation.
Journal of Nonlinear Mathematical Physics 19(2) (2012) 1250010, 22 pp.
- F. Demontis and C. van der Mee,
Closed Form Solutions to the Matrix Sine-Gordon Equation.
IMA Journal of Applied Mathematics, 77, 308-315 (2012). doi: 10.1093/imamat/hxs029.
(click here for further details)
- Francesco Demontis,
,
Exact Solutions to the modified Korteweg-de Vries equation
(see also arxiv.org/abs/1010.1651),
Theoretical and Mathematical Physics 168(1): 886-897 (2011).
- F. Demontis and Cornelis van der Mee,
Exact Solutions to the Integrable Discrete Nonlinear Schrödinger Equation
under a Quasiscalarity Condition,
Communications in Applied and Industrial Mathematics 2 (2011).
- Tuncay Aktosun, Theresa Busse, Francesco Demontis, and Cornelis van der Mee,
Symmetries for exact solutions to the nonlinear
Schrödinger equation, Journal of Physics A, 43, 025202 (2010).
- Tuncay Aktosun, Francesco Demontis, and Cornelis van der Mee,
Exact solutions to the Sine-Gordon Equation,
Journal Mathematical Physics 51, 123521 (2010).
- Francesco Demontis and Cornelis van der Mee,
Wave Operators for Defocusing Matrix Zakharov-Shabat
Systems with Potentials Nonvanishing
at Infinity, Serdica Mathematical Journal, 36, 265-284 (2010).
- Francesco Demontis and Cornelis van der Mee, Scattering
operators for matrix Zakharov-Shabat systems, Integral Equations and
Operator Theory 62(4), 517-540 (2008).
- Francesco Demontis and Cornelis van der Mee, Explicit
solutions of the cubic matrix nonlinear Schrödinger equation,
Inverse Problems 24, 02520 (2008), 16 pp.
DOI: 10.1088/0266-5611/24/2/02520.
- Francesco Demontis and Cornelis van der Mee, Marchenko
equations and norming constants of the matrix Zakharov-Shabat system,
Operators and Matrices 2, 79-113 (2008).
- Tuncay Aktosun, Francesco Demontis, and Cornelis van der Mee,
Exact solutions to the focusing nonlinear Schrödinger
equation, Inverse Problems 23, 2171-2195 (2007).
- Francesco Demontis and Sebastiano Pennisi, On
a further condition in the macroscopic extended model for ultrarelativistic
gases, Ann. Univ. Ferrara Sez. VII Sci. Mat. 53, no. 1, 51-64
(2007).
- M.C. Carrisi, F. Demontis, and A. Scanu, A
kinetic type extended model for dense gases and macromolecular fluids,
Le Matematiche (Catania) 60, no. 1, 181-188 (2006).
- Book's chapter:
- F. Demontis, C. der Mee and F. Vitale,
On the Location of the Discrete Eigenvalues for Defocusing
Zakharov-Shabat Systems having Potentials with
Nonvanishing Boundary Conditions Contemporary Mathematics 635,
Amer. Math. Soc., Providence, RI, 2015. Title of the book: Nonlinear Wave Equations: Analytic and Computational Techniques.
- Tuncay Aktosun, Theresa Busse, Francesco Demontis, and Cornelis van der Mee,
Exact solutions to the nonlinear Schrödinger
equation, In: Joseph A. Ball, Vladimir Bolotnikov, J. William Helton, Leiba Rodman,
and Ilya Spitkovsky (eds.), Topics in Operator Theory, Vol. 2,
Systems and Mathematical Phisics,
Birkhäuser OR 203, Basel and Boston, 2010, pp. 1-12.
- M.C. Carrisi, F. Demontis, S. Pennisi, and A. Scanu,
A kinetic type extended model for polarizable and
magnetizable fluids, Scientific Computing in Electrical Engineering, Mathematics in Industry, Springer, Berlin, 2006, Volume 9, Part IV, 295-300,
DOI: 10.1007/978-3-540-32862-9_42
- Proceedings articles:
- Francesco Demontis and Cornelis van der Mee,
Novel Formulation of Inverse Scattering and Characterization of Scattering Data,
In: Wei Feng, Zhaosheng Feng, Maurizio Grasselli, Akif Ibragimov, Xin Lu,
Stefan Siegmund and Jürgen Voigt (eds.), Dynamical System and Differential
Equations, DCDS Supplement 2011 Proceedings of the 8th AIMS International Conference
(Dresden, Germany), pp. 343-350. September 2011, Clothcover, 1476 pages.
- F. Demontis, S. Pennisi, and F. Rundo, Some
further considerations on the Galilean relativity principle in extended
thermodynamics. In: "WASCOM 2005," 13th Conference on Waves and
Stability in Continuous Media, pp. 176-181, World Sci. Publ., Hackensack, NJ,
2006.
- M.C. Carrisi, F. Demontis, and S. Pennisi, The
non-relativistic limit of relativistic extended thermodynamics with many
moments. II. How it includes the mass, momentum and energy
conservation. In: "WASCOM 2005," 13th Conference on Waves and Stability
in Continuous Media, pp. 95-100, World Sci. Publ., Hackensack, NJ, 2006.
- F. Borghero, F. Demontis, and S. Pennisi, The
non-relativistic limit of relativistic extended thermodynamics with many
moments. I. The balance equations. In: "WASCOM 2005," 13th Conference
on Waves and Stability in Continuous Media, pp. 47-52, World Sci. Publ.,
Hackensack, NJ, 2006.
- F. Borghero, F. Demontis, and S. Pennisi, An exact
macroscopic extended model with many moments for ultrarelativistic
gases. In: "WASCOM 2003," 12th Conference on Waves and Stability in
Continuous Media, pp. 94-101, World Sci. Publ., River Edge, NJ, 2004.
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