A Two-Soliton with Transient Turbulent Regime for the Cubic Half-wave Equation on The Real Line

Patrick Gérard, Enno Lenzmann, Oana Pocovnicu +1

We consider the focusing cubic half-wave equation on the real line $$i{\partial }_{t}u+|D|u=|u{|}^{2}u,\widehat{|D|u}(\xi )=|\xi |\hat{u}(\xi ),(t,x)\in {\mathbb{R}}_{+}\times \mathbb{R}.$$ We…