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math.AP2026
Gauge transform for the Korteweg-de Vries equation and well-posedness below the -scale
Andreia Chapouto, Simão Correia, João Pedro Ramos
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,…
math.AP2024
Sharp blow-up stability for self-similar solutions of the modified Korteweg-de Vries equation
Simão Correia, Raphaël Côte
We consider the modified Korteweg-de Vries equation. Given a self-similar solution, and a subcritical perturbation of any size, we prove that there exists a unique solution to the…