Description
The nonlinear propagation of random dispersive waves has been an active research topic in nonlinear physics since the 1960s. Historically, a very important part of the work on this subject has been focused on weak wave turbulence. Wave turbulence theory deals with the non-equilibrium statistics of incoherent and weakly nonlinear dispersive waves in non-integrable systems. On the other hand, many physical systems are described at leading order by partial differential equations (such as the nonlinear 1D Schrodinger equation) that are integrable in the sense that they can be solved using the inverse scattering transform (IST) method. Nowadays, the theoretical description of nonlinear random wave fields in integrable systems is addressed in the framework of so-called "integrable turbulence", a research area introduced by Zakharov in 2009. In this talk, I will review experimental and numerical developments on the subject of integrable turbulence with a focus on the topic of soliton gas.
