Gino Biondini

Professor, Associate Chair
PhD, Theoretical Physics, University of Perugia, Italy

Contact Information:

324 Mathematics Building
University at Buffalo
Buffalo, NY 14260-2900

Tel:  (716) 645-8810 
Fax: (716) 645 5039

E-mail: biondini@buffalo.edu
Personal website: Gino Biondini

Research

Applied mathematics, nonlinear waves, solutions, 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.

Selected Publications

G Biondini and D Mantzavinos, "Universal nature of the nonlinear stage of modulational instability", Phys. Rev. Lett. 116, 043902 [5 pages] (2016) 

G Biondini, D K Kraus and B Prinari, "The three-component defocusing nonlinear Schrodinger equation with nonzero boundary conditions" (2015), arxiv:1511.02885 [nlin.si]

G Biondini and T Trogdon, "Gibbs phenomenon for dispersive PDEs" (2015), arxiv:1411.6142 [math.ap]

G Biondini and E Fagerstrom, The integrable nature of modulational instability", SIAM J. Appl. Math. 75, 136-163 (2015) 

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)

Z Marzec, J Schuster, G Biondini and W L Kath, "Hybrid hinge model for polarization-mode dispersion in installed optical fiber transmission systems", IEEE J. Lightwave Technol. 32 1412-1419 (2014)

D Wang, J-H Jung and G Biondini, "Detailed comparison of numerical methods for the perturbed sine-Gordon equation with impulsive forcing", J. Eng. Math. 87, 167-186 (2014)

G. Biondini and G. Hwang, "Solitons, boundary value problems and a nonlinear method of images", J. Phys. A 42, 205207 [18 pages] (2009)  [cited 7 times]

G Biondini, "Line soliton interactions of the Kadomtsev-Petviashvili equation", Phys. Rev. Lett. 99, 064103 [4 pages] (2007)  [cited 19 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 17 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 34 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 55 times]

G Biondini, W L Kath and C R Menyuk, "Importance sampling for polarization-mode dispersion", Photon. Technol. Lett. 14, 310-312 (2002)  [cited 62 times]

G Biondini and M J Ablowitz, "Multiple scale dynamics in strongly dispersion-managed communication systems", Opt. Lett. 23, 1668-1670 (1998)  [cited 165 times]