Professor & Department Chair

Applied mathematics, nonlinear waves, solitons, integrable systems, inverse problems, applied probability, stochastic processes, optics.

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", SIAM Rev. **60**, 888--908 (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) [cited 14 times]

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 41 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 water", Phys. Rev. Lett. **117**, 144102 (2016) [cited 18 times]

**G. Biondin**i and E. Fagerstrom, "The integrable nature of modulational instability", SIAM J. Appl. Math. **75**, 136-163 (2015) [cited 25 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 (2014) [cited 57 times]

**G. Biondini** and G. Hwang, "Solitons, boundary value problems and a nonlinear method of images", *J. Phys. A* **42**, 205207 (2009) [cited 15 times]

**G. Biondini**, "Line soliton interactions of the Kadomtsev-Petviashvili equation", Phys. Rev. Lett. **99**, 064103 (2007) [cited 33 times]

J. Li, E. Spiller and **G. Biondini**, "Noise-induced perturbations of dispersion-managed solitons", Phys. Rev. A **75**, 053818 (2007) [cited 15 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 25 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 (2006) [cited 60 times]

**G. Biondini** and S. Chakravarty, "Soliton solutions of the Kadomtsev-Petviashvili II equation", J. Math. Phys. **47**, 033514 (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 70 times]

**G. Biondini**, W. L. Kath and C. R. Menyuk, "Importance sampling for polarization-mode dispersion", Photon. Technol. Lett. **14**, 310-312 (2002) [cited 64 times]

**G. Biondini** and M. J. Ablowitz, "Multiscale pulse dynamics in communication systems with strong dispersion management", Opt. Lett. **23**, 1668-1670 (1998) [cited 178 times]