Solitonic models of nonlinear phenomena: recent results and perspectives

The concept of a diluted soliton gas was introduced in 1971 by V.E. Zakharov as an infinite collection of weakly interacting solitons. More recently, this concept has been extended to dense gases, in which solitons interact strongly and continuously. In the last few years, this field of studies has attracted a rapidly growing interest from both theoretical and experimental points of view. One of the main reasons for this change is the development of numerical algorithms, which made it possible for the first time to simulate wave dynamics of a dense soliton gas. With the help of these algorithms, it has been demonstrated recently that soliton gas dynamics underlies some fundamental nonlinear wave phenomena, such as the spontaneous modulation instability and formation of rogue waves. In my talk, I am going to review recent results and outline perspectives for the current studies of soliton gas, demonstrating that solitonic models might be the key to solving some of the oldest and most pertinent problems in the nonlinear waves theory.

Bio: I received my PhD at the Landau Institute for Theoretical Physics in Moscow, worked as a postdoctoral researcher in France and Russia, and then joined the Shirshov Institute of Oceanology in Moscow as a senior researcher and then leading researcher. Currently, I am a visiting researcher at Northumbria University under the Solidarity Programme funded jointly by the Isaac Newton Institute for Mathematical Sciences and London Mathematical Society. I work on integrable turbulence, soliton gas and rogue waves with applications to ocean dynamics and nonlinear optics.