I will discuss a novel type of a derivative nonlinear Schrödinger type equation, which can be seen as a continuum limit of completely integrable Calogero-Moser systems. In this talk, I will focus on dynamics of $N$-soliton solutions, turbulence (growth of Sobolev norms), and a Lax pair structure. This is ongoing joint work with Patrick Gérard (Orsay).
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