“Solitons are special solutions of integrable PDEs and, due to their stability, they appear frequently in physical systems (e.g., water waves, optical fibers, condensed matter physics, etc.). But what happens if we have an infinite number of solitons? This was the question that Zakharov attempted to answer in 1971, and it opened a new line of research in the field of integrable systems.
In this talk, we will present some contemporary results in the study of this kind of solution, also known as soliton gas solutions, for the Nonlinear Schrödinger Equation (NLS), using techniques from Inverse Scattering Theory (IST) and complex analysis (e.g., Riemann-Hilbert problems, d-bar problems, etc.). We will show that, depending on where the solitons condense, various phenomena and asymptotic scenarios emerge. Some examples will be presented: the case where the solitons condense in a disk, and the case where they condense on an ellipse.
This is joint work with Prof. Tamara Grava (University of Bristol, SISSA), Prof. Marco Bertola (Concordia University), and Prof. Minakov (Charles University).”
