## Nonlinear spectral synthesis of breather gas in focusing NLS equation: a numerical approach

#### Giacomo Roberti

### Abstract:

Soliton gas was introduced by Zakharov [Sov. Phys. JETP 33, 538 (1971)] as an infinite ensemble of interacting KdV solitons randomly distributed in velocity and positions. This concept has been extended by El and Tovbis [arXiv:1910.05732] in their development of the spectral theory of soliton and breather gases in the framework of the focusing Nonlinear Schrodinger equation. Moreover, it has been shown in a recent work by Gelash et al. [PRL, 123, 234102 (2019)] how the spectral soliton gas formalism could lead to a new understanding of the evolution of random processes in integrable systems, the so-called integrable turbulence.

In this context, the ability to numerically build the soliton and breather gas solutions from the nonlinear spectral plane is a key element for testing the mathematical model and investigate its physical applications.

In this work, we focused on the numerical synthesis of breather gases from the corresponding finite-gap spectrum. We were able to verify the theoretically predicted values of the phase shift in two-breather interactions and the effective velocity of a trial breather propagating through a uniform breather gas. This is joint work with P. Suret, S. Randoux, G. El and A. Tovbis.