Open AccessThe fundamental problem of inverse scattering method in solving the DNLS equation
Author(s) -
He Jin-Chun,
Zongyun Chen,
Nian-Ning Huang
Publication year - 2009
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.58.6063
Subject(s) - inverse scattering transform , inverse scattering problem , orthonormal basis , inverse problem , inverse , quantum inverse scattering method , physics , scattering , mathematical analysis , scattering theory , mathematics , quantum mechanics , geometry
This is a basic work on the inverse scattering transform that constructs the complete orthonormal system of the free Jost solution. In order to establish the system for the DNLS equation, we introduce a new transform for the spectral parameter and a gauge transform. The Marchenko's equation and the Zakharov-Shabat's equation of inverse scattering are derived based on the new spectral parameter.