Gauge transform for the Korteweg-de Vries equation and well-posedness below the $H^{-1}$-scale

Andreia Chapouto, Simão Correia, Simão Correia +2

We propose a new formulation of the Korteweg-de Vries equation (KdV) on the real line, via a gauge transform. While KdV and the gauged equation are equivalent for smooth solutions,…