Dressing method and quadratic bundles related to symmetric spaces. Vanishing boundary conditions

We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)x U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear Schroedinger equation which serves as a motivational example for...

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Bibliographic Details
Published in:arXiv.org 2014-10
Main Author: Valchev, Tihomir
Format: Article
Language:English
Subjects:
Boundary conditions
Bundles
Decay rate
Nonlinear equations
Schrodinger equation
Online Access:Get full text
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Summary:We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m)x U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear Schroedinger equation which serves as a motivational example for our general considerations. We extensively discuss how one can apply Zakharov-Shabat's dressing procedure to derive reflectionless potentials obeying zero boundary conditions. Those could be used for one to construct fast decaying solutions to any nonlinear equation belonging to the same hierarchy. One can distinguish between generic soliton type solutions and rational solutions.
ISSN:2331-8422
DOI:10.48550/arxiv.1410.5350