João P. G. Ramos

activity

20242026

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math.AP2026

Phase retrieval for Schrödinger evolutions

Ben Pineau, João P. G. Ramos, Mitchell A. Taylor

Consider the one-dimensional Schrödinger evolution $i \partial_{t} w + \partial_{x}^{2} w = V w, (t, x) \in [0, T] \times R,$ where $V$ is a real-valued time-dependent potentia…

math.AP2026

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

Phase retrieval for Schrödinger evolutions

Gauge transform for the Korteweg-de Vries equation and well-posedness below the H−1-scale

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