A discrete Schrödinger spectral problem and associated evolution equations

M. Boiti; M. Bruschi; F. Pempinelli; B. Prinari

doi:10.1088/0305-4470/36/1/309

A discrete Schrödinger spectral problem and associated evolution equations

M. Boiti
, M. Bruschi
, F. Pempinelli
, B. Prinari

Mathematics

National Institute for Nuclear Physics
University of Rome La Sapienza

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

Abstract

A recently proposed discrete version of the Schrödinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated with this spectral problem is derived. It is shown that a discrete version of the KdV, sine-Gordon and Liouville equations is included and that the so-called 'inverse' class in the hierarchy is local. The whole class of related Darboux and Bäcklund transformations is also exhibited.

Original language	English
Pages (from-to)	139-149
Number of pages	11
Journal	Journal of Physics A: Mathematical and General
Volume	36
Issue number	1
DOIs	https://doi.org/10.1088/0305-4470/36/1/309
State	Published - Jan 10 2003

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abstract = "A recently proposed discrete version of the Schr{\"o}dinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated with this spectral problem is derived. It is shown that a discrete version of the KdV, sine-Gordon and Liouville equations is included and that the so-called 'inverse' class in the hierarchy is local. The whole class of related Darboux and B{\"a}cklund transformations is also exhibited.",

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N2 - A recently proposed discrete version of the Schrödinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated with this spectral problem is derived. It is shown that a discrete version of the KdV, sine-Gordon and Liouville equations is included and that the so-called 'inverse' class in the hierarchy is local. The whole class of related Darboux and Bäcklund transformations is also exhibited.

AB - A recently proposed discrete version of the Schrödinger spectral problem is considered. The whole hierarchy of differential-difference nonlinear evolution equations associated with this spectral problem is derived. It is shown that a discrete version of the KdV, sine-Gordon and Liouville equations is included and that the so-called 'inverse' class in the hierarchy is local. The whole class of related Darboux and Bäcklund transformations is also exhibited.

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A discrete Schrödinger spectral problem and associated evolution equations

Abstract

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