Professor, Associate Chair
PhD, Theoretical Physics, University of Perugia, Italy
Applied mathematics, nonlinear waves, solitons, integrable systems, inverse problems, applied probability, stochastic processes, optics.
The study of physical phenomena by means of mathematical models often leads to certain nonlinear partial differential equations which reveal a surprisingly rich mathematical structure. The study of these equations thus offers a unique combination of interesting mathematics and concrete physical/technological applications.
Professor Biondini's research has two main goals: The first goal is to understand the properties of these equations and their solutions. This kind of research is usually called the study of "integrable systems", and requires a combination of techniques from different branches of mathematics. The second goal is to study the application of these nonlinear and/or stochastic systems to concrete physical situations, with the aim of obtaining results of practical usefulness. This often requires studying the combined effects of several kinds of perturbations which are often stochastic in nature, and can be done using exact methods, approximations (such as modeling, asymptotics and perturbative techniques), numerical methods (numerical modeling, Monte-Carlo simulations and variance reduction techniques) or combinations of all these approaches. Specific applications considered by Prof. Biondini are optical fiber communications, nonlinear optics and water waves.
G. Biondini, S. Li, D. Mantzavinos and S. Trillo, "Universal behavior of modulationally unstable media", arXiv:1710.05068 [nlin.ps], to appear in SIAM Review (2018)
G. Biondini and D. Mantzavinos, "Long-time asymptotics for the focusing nonlinear Schrodinger equation with nonzero boundary conditions at infinity and asymptotic stage of modulational instability", Commun. Pure Appl. Math. 70, 2300--2365 (2017)
M. J. Ablowitz, G. Biondini and Q. Wang, "Whitham modulation theory for the Kadomtsev-Petviashvili equation", Roy. Soc. Proc. A 473, 20160695 (2017)
G. Biondini and T. Trogdon, "Gibbs phenomenon for dispersive PDEs", SIAM J. Appl. Math. 77, 813--817 (2017)
G. Biondini and D. Mantzavinos, "Universal nature of the nonlinear stage of modulational instability", Phys. Rev. Lett. 116, 043902 [5 pages] (2016) [cited 19 times]
G. Biondini, D. K. Kraus and B. Prinari, "The three-component defocusing nonlinear Schrodinger equation with nonzero boundary conditions", Commun. Math. Phys. 348, 475--533 (2016)
S. Trillo, G. Deng, G. Biondini M. Klein, A. Chabchoub and M. Onorato, "Experimental observation and theoretical description of multi-soliton fission in shallow waterâ€, Phys. Rev. Lett. 117, 144102 (2016) [cited 13 times]
G. Biondini and E. Fagerstrom, The integrable nature of modulational instability", SIAM J. Appl. Math. 75, 136-163 (2015) [cited 14 times]
G. Biondini and G. Kovacic, Inverse scattering transform for the focusing nonlinear Schrodinger equation with non-zero boundary conditions", J. Math. Phys. 55 031506 [22 pages] (2014) [cited 34 times]
G. Biondini and G. Hwang, "Solitons, boundary value problems and a nonlinear method of images", J. Phys. A 42, 205207 [18 pages] (2009) [cited 10 times]
G. Biondini, "Line soliton interactions of the Kadomtsev-Petviashvili equation", Phys. Rev. Lett. 99, 064103 [4 pages] (2007) [cited 28 times]
J. Li, E. Spiller and G. Biondini, "Noise-induced perturbations of dispersion-managed solitons", Phys. Rev. A 75, 053818: [13 pages] (2007) [cited 12 times]
G. Biondini and Y. Kodama, "On the Whitham equations for the defocusing nonlinear Schroedinger equation with step initial data", J. Nonlin. Sci. 16, 435-481 (2006) [cited 21 times]
B. Prinari, M. J. Ablowitz and G. Biondini, "Inverse scattering transform for the vector nonlinear Schroedinger equation with nonvanishing boundary conditions", J. Math. Phys. 47, 063508:1-33 (2006) [cited 50 times]
G. Biondini and S. Chakravarty, "Soliton solutions of the Kadomtsev-Petviashvili II equation", J. Math. Phys. 47, 033514:1-26 (2006) [cited 51 times]
G. Biondini and Y. Kodama, "On a family of solutions of the Kadomtsev-Petviashvili equation which also satisfy the Toda lattice hierarchy", J. Phys. A 36, 10519-10536 (2003) [cited 62 times]
G. Biondini, W. L. Kath and C. R. Menyuk, "Importance sampling for polarization-mode dispersion", Photon. Technol. Lett. 14, 310-312 (2002) [cited 60 times]
G. Biondini and M. J. Ablowitz, "Multiple scale dynamics in strongly dispersion-managed communication systems", Opt. Lett. 23, 1668-1670 (1998) [cited 172 times]