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Symplectic nonsqueezing for the KdV flow on the line

Maria Ntekoume

Vol. 4 (2022), No. 3, 401–448
Abstract

We show symplectic nonsqueezing for the KdV equation on the line . This is achieved via finite-dimensional approximation. Our choice of finite-dimensional Hamiltonian system that effectively approximates the KdV flow is inspired by the recent breakthrough of Killip and Vişan (Ann. of Math. (2) 190:1 (2019), 249–305) in the well-posedness theory of the equation in low-regularity spaces, relying on its completely integrable structure. The employment of our methods also provides us with a new concise proof of symplectic nonsqueezing for the same equation on the circle 𝕋, recovering the result of Colliander et al. (Acta Math. 195 (2005), 197–252).

Keywords
KdV, symplectic nonsqueezing, finite-dimensional approximation
Mathematical Subject Classification
Primary: 35Q53
Milestones
Received: 17 July 2020
Revised: 19 January 2022
Accepted: 10 March 2022
Published: 4 December 2022
Authors
Maria Ntekoume
Department of Mathematics
Rice University
Houston, TX
United States