Inverse Scattering Transform is a powerful method to exactly solve nonlinear partial differential equations, including the nonlinear Schrödinger equation which is the master model describing light propagation in optical fibers. Currently most of the internet data traffic flows in form of light pulses through optical fibers on earth and below the oceans and the demand of an increase of transmitted information data rate requires increasing the optical power traveling through optical fibers. Such power increase causes an increase of the nonlinearity which in turn implies a distortion of the signal with a corresponding degradation of its information content: this is because in present communications systems the information is encoded in eigendmodes of a linear channel, treating the fibre nonlinearity as an undesired perturbation.

An alternative approach, initiated in the seminal work by Hasegawa and Nyu in 1993 aims at encoding the information in nonlinear eigendmodes (the so called nonlinear spectrum, or scattering data) of the channel, recognizing the full nonlinear nature of the optical fibre. The information is encoded in such a way that, despite the fact that the light waveform suffers substantial changes upon propagation from the transmitter to the receiver, the information content is not lost. The information can be then recovered at the receiver by performing mathematical operations on the received signal.

Inverse Scattering Transform (or Nonlinear Fourier Transform as it is called in engineering community) allows to encode information in the so called nonlinear spectrum of the signal. At the moment such technique is still at the research level and it is not clear if it could become commercial one day, but it is anyway worth having a look about it (at least for the beauty of the math involved).

#### My works in this field:

- S. Gaiarin, A. M. Perego, E. P. da Silva, F. Da Ros and D. Zibar “Dual-polarization nonlinear Fourier-transform-based optical communication system ”,
*Optica*5, 263 (2018).