Darboux Transformation: New Identities

This letter reports some new identities for multisoliton potentials that are based on the explicit representation provided by the Darboux matrix. These identities can be used to compute the complex gradient of the energy content of the tail of the profile with respect to the discrete eigenvalues and...

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Bibliographic Details
Published in:arXiv.org 2019-01
Main Author: Vaibhav, Vishal
Format: Article
Language:English
Subjects:
Complex variables
Eigenvalues
Online Access:Get full text
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Summary:This letter reports some new identities for multisoliton potentials that are based on the explicit representation provided by the Darboux matrix. These identities can be used to compute the complex gradient of the energy content of the tail of the profile with respect to the discrete eigenvalues and the norming constants. The associated derivatives are well defined in the framework of the so-called Wirtinger calculus which can aid a complex variable based optimization procedure in order to generate multisolitonic signals with desired effective temporal and spectral width.
ISSN:2331-8422
DOI:10.48550/arxiv.1901.01037