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An algebraic background for construction of hierarchies of PDE in dimension (2|1) Roger, Claude

Description

In d=2 with variables (x,t), the superalgebraic trick of adding a supplementary odd variable allows the construction of a "square root of time", an operator D satisfying D^2=∂/∂t in superspace of dimension (2|1). We used it to obtain a Miura transform in dimension (2|1) for non stationary Schrödinger type operators. We shall discuss here the construction of an algebra of pseudodifferential symbols in dimension (2|1); that algebra generalizes the one for d=1, used in construction of hierarchies from isospectral deformations of stationary Schrödinger type operators.

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Title
An algebraic background for construction of hierarchies of PDE in dimension (2|1)
Creator
Roger, Claude
Publisher
Banff International Research Station for Mathematical Innovation and Discovery
Date Issued
2016-06-16T11:01
Description
In d=2 with variables (x,t), the superalgebraic trick of adding a supplementary odd variable allows the construction of a "square root of time", an operator D satisfying D^2=∂/∂t in superspace of dimension (2|1). We used it to obtain a Miura transform in dimension (2|1) for non stationary Schrödinger type operators. We shall discuss here the construction of an algebra of pseudodifferential symbols in dimension (2|1); that algebra generalizes the one for d=1, used in construction of hierarchies from isospectral deformations of stationary Schrödinger type operators.
Extent
42 minutes
Subject
Mathematics; Dynamical systems and ergodic theory; Ordinary differential equations; Dynamical systems
Type
Moving Image
File Format
video/mp4
Language
eng
Notes
Author affiliation: Universite Claude Bernard ( Lyon 1)
Series
BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))
Date Available
2017-01-28
Provider
Vancouver : University of British Columbia Library
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
DOI
10.14288/1.0340388
URI
http://hdl.handle.net/2429/60033
Affiliation
Non UBC
Peer Review Status
Unreviewed
Scholarly Level
Faculty
Rights URI
http://creativecommons.org/licenses/by-nc-nd/4.0/
Aggregated Source Repository
DSpace

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Attribution-NonCommercial-NoDerivatives 4.0 International