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Canonical Structure of Integrable Systems — Revisited
Author(s) -
Roy Swapna,
Chowdhury A. Roy
Publication year - 1988
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190360902
Subject(s) - integrable system , eigenfunction , mathematics , inverse scattering transform , symplectic geometry , inverse scattering problem , quantum inverse scattering method , nonlinear system , continuous spectrum , formalism (music) , soliton , square integrable function , mathematical analysis , inverse , mathematical physics , eigenvalues and eigenvectors , physics , inverse problem , quantum mechanics , geometry , art , musical , visual arts
We have reanalysed and reviewed the canonical structure associated with nonlinear integrable equations with emphasis on the mutual influence between the discrete and continuous spectrum. Our derivation explains the use of square eigenfunctions in the derivation of the symplectic structure. Actually we have illustrated the whole formalism on the basis of Derivative Nonlinear Schrödinger equation. It is really surprising to note that the usual approach to soliton‐soliton scattering is not canonical. Furthermore an absolute separation of the discrete and continuous spectrum at least in case of DNLSE is not consistent. Our analysis really points out some basic difficulty in the framework Inverse Scattering Transform.