Book Review: The defocusing NLS equation and its normal form

DOI10.1090/bull/1522zbMath1332.00014OpenAlexW2314807537MaRDI QIDQ2797795

Dario Bambusi

Publication date: 31 March 2016

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/bull/1522

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) NLS equations (nonlinear Schrödinger equations) (35Q55) Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions for ordinary differential operators (34L20) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) External book reviews (00A17)

Cites Work

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• Fibration of the phase space for the Korteweg-de Vries equation
• On the symplectic structure of the phase space for periodic KdV, Toda, and defocusing NLS
• Canonically Conjugate Variables for the Korteweg-de Vries Equation and the Toda Lattice with Periodic Boundary Conditions
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• [https://portal.mardi4nfdi.de/wiki/Publication:4342735 Action-angle variables for the cubic Schr�dinger equation]

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