About the Quadratic Szegö Hierarchy

DOI10.1137/18M1179134zbMath1501.37070arXiv1804.01261MaRDI QIDQ4632550

Joseph Thirouin

Publication date: 30 April 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.01261

zbMATH Keywords

complete integrabilitygrowth of Sobolev normsSzegö equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Dynamical systems approach to turbulence (76F20) Control of turbulent flows (76F70)

Cites Work

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• Invariant tori for the cubic Szegö equation
• On the growth of Sobolev norms of solutions of the fractional defocusing NLS equation on the circle
• Explicit formula for the solution of the Szegö equation on the real line and applications
• Conformal flow on \(\mathrm{S}^{3}\) and weak field integrability in \(\mathrm{AdS}_{4}\)
• Classification of traveling waves for a quadratic Szegö equation
• The defocusing NLS equation and its normal form
• Long-time instability and unbounded Sobolev orbits for some periodic nonlinear Schrödinger equations
• Large-time blowup for a perturbation of the cubic Szegő equation
• The cubic Szegő equation
• The cubic szego equation and hankel operators
• An explicit formula for the cubic Szegő equation

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