Strange tori of the derivative nonlinear Schrödinger equation
type: Item
instance of: scholarly article
title: Strange tori of the derivative nonlinear Schrödinger equation
zbMATH Open document ID: 1134.35100
author: Y. Charles Li
published in: Letters in Mathematical Physics
publication date: 2007-05-31T00:00:00Z
review text: Derivative nonlinear Schrödinger equation \(i q_t = q_{xx} - i (| q| ^2 q)_x\) is investigated along the lines of the book [Chaos in partial differential equations, Somerville, MA: International Press (2003; Zbl 1043.35001)] by the same author. Under periodic boundary conditions, Floquet theory is applicable to the Lax equation. As the main result of the paper, tori and their whiskers generated by means of iterated Darboux transformation are shown to exhibit unusual properties: One level set of the Floquet discriminant can contain disconnected tori of different dimensions. Diffusion (variation of invariants) along the tori under small perturbations of the equation is also studied. Finally, the open problem of invariant manifolds is discussed.
reviewed by: Michal Marvan
Mathematics Subject Classification ID: 35Q55
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 5159814
zbMATH Keywords: strange torus
zbMATH Keywords: derivative nonlinear Schrödinger equation
zbMATH Keywords: Lax pair
zbMATH Keywords: Darboux transformation
zbMATH Keywords: Floquet theory
MaRDI profile type: Publication
full work available at URL: s11005-007-0152-4
OpenAlex ID: W2110545925
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DOI: 10.1007/S11005-007-0152-4
description: scientific article; zbMATH DE number 5159814