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Klaus-Shaw potentials for the Ablowitz-Ladik lattice Espínola-Rocha, Jesús Adrián
Description
Some PDEs and ODEs admit a Lax pair (a pair of linear operators) to be completely solve the equation. One of these operators defines a spectral problem. For some equations (as for the Korteweg-deVries, KdV, equation) this operator is self-adjoint and, consequently, its discrete spectrum is real. However, for some other equations, this operator is non-selfadjoint, such as for the nonlinear Schrödinger (NLS) equation or the Ablowitz-Ladik equation. In 2001, M. Klaus and J. K. Shaw found symmetries and conditions on the potentials for the Zakharov-Shabat system (spectral problem for the NLS equation) for the eigenvalues to lie on the imaginary axis. In this talk, I will show which would be an equivalent to the Klaus-Shaw theorem for the Ablowitz-Ladik lattice. This is a work in progress. This is a joint work with P. Shipman (Colorado State University) and S. Shipman (Louisiana State University).
Item Metadata
Title |
Klaus-Shaw potentials for the Ablowitz-Ladik lattice
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2017-06-22T15:30
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Description |
Some PDEs and ODEs admit a Lax pair (a pair of linear operators) to be completely solve the equation. One of these operators defines a spectral problem. For some equations (as for the Korteweg-deVries, KdV, equation) this operator is self-adjoint and, consequently, its discrete spectrum is real. However, for some other equations, this operator is non-selfadjoint, such as for the nonlinear Schrödinger (NLS) equation or the Ablowitz-Ladik equation. In 2001, M. Klaus and J. K. Shaw found symmetries and conditions on the potentials for the Zakharov-Shabat system (spectral problem for the NLS equation) for the eigenvalues to lie on the imaginary axis. In this talk, I will show which would be an equivalent to the Klaus-Shaw theorem for the Ablowitz-Ladik lattice. This is a work in progress. This is a joint work with P. Shipman (Colorado State University) and S. Shipman (Louisiana State University).
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Extent |
28 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Universidad Autonoma de Metropolitana -Azcapotzalco
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Series | |
Date Available |
2017-12-20
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0362145
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International