Professor

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.

A. Abeya, **G. Biondini,** G. Kovačič and B. Prinari “Inverse scattering transform for two-level systems with one-sided nonzero background”, Communications in Mathematical Physics 405, 192 (2024)

A. Romero-Ros, G. C. Katsimiga, S. I. Mistakidis, S. Mossman, **G. Biondini,** P. Schmelcher, P. Engels and P. G. Kevrekidis, “Experimental realization of the Peregrine soliton in repulsive two-component Bose-Einstein condensates”, Physical Review Letters 132, 033402 (2024)

**G. Biondini,** X.-D. Luo, J. Oregero and A. Tovbis, “Elliptic finite-band potentials of a non-self-adjoint Dirac operator”, Advances in Mathematics 429, 109188 (2023)

**G. Biondini,** S. Li and D. Mantzavinos, “Long-time asymptotics for the focusing nonlinear Schrödinger equation with non-zero boundary conditions in the presence of a discrete spectrum”, Communications in Mathematical Physics 382, 1495–1577 (2021)

**G. Biondini**, S. Li, D. Mantzavinos and S. Trillo, "Universal behavior of modulationally unstable media", SIAM Review 60, 888--908 (2018) [cited 47 times]

**G. Biondini a**nd D. Mantzavinos, "Long-time asymptotics for the focusing nonlinear Schrodinger equation with nonzero boundary conditions at infinity and asymptotic stage of modulational instability", Communications on Pure Applied Mathematics 70, 2300--2365 (2017) [cited 98 times]

M. J. Ablowitz, **G. Biondini** and Q. Wang, "Whitham modulation theory for the Kadomtsev-Petviashvili equation", Royal Society Proceedings A 473, 20160695 (2017) [cited 26 times]

**G. Biondini** and T. Trogdon, "Gibbs phenomenon for dispersive PDEs", SIAM J. Applied Mathematics 77, 813--817 (2017)

**G. Biondini** and D. Mantzavinos, "Universal nature of the nonlinear stage of modulational instability", Physical Review Letters 116, 043902 (2016) [cited 130 times]

**G. Biondini,** D. K. Kraus and B. Prinari, "The three-component defocusing nonlinear Schrodinger equation with nonzero boundary conditions", Communications in Mathematical Physics 348, 475--533 (2016) [cited 64 times]

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”, Physical Review Letters 117, 144102 (2016) [cited 60 times]

**G. Biondini** and G. Kovačič, Inverse scattering transform for the focusing nonlinear Schrodinger equation with non-zero boundary conditions", J. Mathematical Physics 55 031506 (2014) [cited 238 times]

**G. Biondini** and G. Hwang, "Solitons, boundary value problems and a nonlinear method of images", J. Physics A 42, 205207 (2009) [cited 47 times]

**G. Biondini,** "Line soliton interactions of the Kadomtsev-Petviashvili equation", Physical Review Letters 99, 064103 (2007) [cited 74 times]

J. Li, E. Spiller and **G. Biondini**, "Noise-induced perturbations of dispersion-managed solitons", Physical Review A 75, 053818 (2007) [cited 28 times]

**G. Biondini** and Y. Kodama, "On the Whitham equations for the defocusing nonlinear Schroedinger equation with step initial data", J. Nonlinear Science 16, 435-481 (2006) [cited 51 times]

B. Prinari, M. J. Ablowitz and **G. Biondini,** "Inverse scattering transform for the vector nonlinear Schroedinger equation with nonvanishing boundary conditions", J. Mathematical Physics 47, 063508 (2006) [cited 176 times]

**G. Biondini** and S. Chakravarty, "Soliton solutions of the Kadomtsev-Petviashvili II equation", J. Mathematical Physics 47, 033514 (2006) [cited 126 times]

**G. Biondini** and Y. Kodama, "On a family of solutions of the Kadomtsev-Petviashvili equation which also satisfy the Toda lattice hierarchy", J. Physics A 36, 10519-10536 (2003) [cited 141 times]

**G. Biondini,** W. L. Kath and C. R. Menyuk, "Importance sampling for polarization-mode dispersion", IEEE Photonics Technololgy Letters 14, 310-312 (2002) [cited 118 times]

**G. Biondini** and M. J. Ablowitz, "Multiple scale dynamics in strongly dispersion-managed communication systems", Optics Letters 23, 1668-1670 (1998) [cited 274 times]