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

**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.

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]