**Nonlinear waves and their applications
**
- Overview

- Selected publications

- Highly cited works

- Image gallery

Prof. Biondini's interests are in the field of physical applied mathematics. The study of physical phenomena by means of mathematical models is an essential component of applied mathematics. In a large number of cases, these models lead to a certain class of nonlinear and/or stochastic partial differential equations. The study of these equations is especially attractive because it offers a unique combination of interesting mathematics and concrete physical/technological applications.

Prof. Biondini's research has two distinct but related goals. The first one is to understand the properties of these equations and their solutions and to investigate their surprisingly rich mathematical structure. This line of research often requires a combination of techniques from different branches of pure and applied mathematics. The second goal concerns the application of these nonlinear and/or stochastic differential equations to concrete physical systems, aiming at producing results of practical usefulness. This can be accomplished using exact methods, approximations (such as asymptotics and perturbative methods), numerical simulations or combinations of these approaches. Applications considered by Prof. Biondini are water waves and nonlinear optics.

**
Selected publications**

"Universal nature of the nonlinear stage of modulational instability",

with D. Mantzavinos,

"Importance sampling for dispersion-managed solitons",

with E.T. Spiller,

"Solitons, boundary value problems and a nonlinear method of images",

with G. Hwang,

"Line soliton interactions of the Kadomtsev-Petviashvili equation",

"On the Whitham equations for the defocusing nonlinear Schrodinger equation with step initial data",

with Y. Kodama,

"Inverse scattering transform for the vector nonlinear Schrodinger equation with nonvanishing boundary conditions",

with M. J. Ablowitz and B. Prinari,

"Importance sampling for polarization-mode dispersion: Techniques and applications",

with W. L. Kath and C. R. Menyuk,

[Correction:

"Nonlinear Schroedinger equations with mean terms in non-resonant multi-dimensional quadratic materials",

with M. J. Ablowitz and S. Blair,

**Highly cited works**

"Multiscale dynamics in strongly dispersion-managed communication systems",

with M.J. Ablowitz,

"Importance sampling for polarization-mode dispersion",

with W.L. Kath and C.R. Menyuk,

"On a family of solutions of the Kadomtsev-Petviashvili equation which also satisfy the Toda lattice hierarchy",

with Y. Kodama,

"Four-wave mixing in wavelength-division multiplexed soliton systems: damping and amplification",

with M.J. Ablowitz, S. Chakravarty, R.B. Jenkins and J. Sauer,

"Methods for discrete solitons in nonlinear lattices",

with M.J. Ablowitz and Z.H. Musslimani,

"Soliton solutions of the Kadomtsev-Petviashvili II equation",

with S. Chakravarty,

"Multiple importance sampling for first- and second-order polarization-mode dispersion",

with S.L. Fogal and W.L. Kath,

[Correction:

"On quasi-linear dispersion-managed transmission systems",

with M.J. Ablowitz and T. Hirooka,

Tue Sep 08 2015 14:54:51 GMT-0400 (EDT)