Higher order potential expansion for the continuous limits of the Toda hierarchy

Runliang Lin; Wen-Xiu Ma; Yunbo Zeng

doi:10.1088/0305-4470/35/23/308

Higher order potential expansion for the continuous limits of the Toda hierarchy

Runliang Lin
, Wen-Xiu Ma
, Yunbo Zeng

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

7 Citations (Scopus)

Abstract

A method for introducing the higher order terms in the potential expansion to study the continuous limits of the Toda hierarchy is proposed in this paper. The method ensures that the higher order terms are differential polynomials of the lower ones and can be continued to be performed indefinitely. By introducing the higher order terms, the fewer equations in the Toda hierarchy are needed in the so-called recombination method to recover the KdV hierarchy. It is shown that the Lax pairs, the Poisson tensors and the Hamiltonians of the Toda hierarchy tend towards the corresponding ones of the KdV hierarchy in the continuous limit.
© 2002 IOP Publishing Ltd

Original language	English
Pages (from-to)	4915-4928
Journal	Journal of Physics A: Mathematical and General
Volume	35
Issue number	23
DOIs	https://doi.org/10.1088/0305-4470/35/23/308
Publication status	Published - 14 Jun 2002
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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abstract = "A method for introducing the higher order terms in the potential expansion to study the continuous limits of the Toda hierarchy is proposed in this paper. The method ensures that the higher order terms are differential polynomials of the lower ones and can be continued to be performed indefinitely. By introducing the higher order terms, the fewer equations in the Toda hierarchy are needed in the so-called recombination method to recover the KdV hierarchy. It is shown that the Lax pairs, the Poisson tensors and the Hamiltonians of the Toda hierarchy tend towards the corresponding ones of the KdV hierarchy in the continuous limit. {\textcopyright} 2002 IOP Publishing Ltd",

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AU - Lin, Runliang

AU - Ma, Wen-Xiu

AU - Zeng, Yunbo

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

PY - 2002/6/14

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N2 - A method for introducing the higher order terms in the potential expansion to study the continuous limits of the Toda hierarchy is proposed in this paper. The method ensures that the higher order terms are differential polynomials of the lower ones and can be continued to be performed indefinitely. By introducing the higher order terms, the fewer equations in the Toda hierarchy are needed in the so-called recombination method to recover the KdV hierarchy. It is shown that the Lax pairs, the Poisson tensors and the Hamiltonians of the Toda hierarchy tend towards the corresponding ones of the KdV hierarchy in the continuous limit. © 2002 IOP Publishing Ltd

AB - A method for introducing the higher order terms in the potential expansion to study the continuous limits of the Toda hierarchy is proposed in this paper. The method ensures that the higher order terms are differential polynomials of the lower ones and can be continued to be performed indefinitely. By introducing the higher order terms, the fewer equations in the Toda hierarchy are needed in the so-called recombination method to recover the KdV hierarchy. It is shown that the Lax pairs, the Poisson tensors and the Hamiltonians of the Toda hierarchy tend towards the corresponding ones of the KdV hierarchy in the continuous limit. © 2002 IOP Publishing Ltd

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DO - 10.1088/0305-4470/35/23/308

M3 - RGC 21 - Publication in refereed journal

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VL - 35

SP - 4915

EP - 4928

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 23

ER -

Higher order potential expansion for the continuous limits of the Toda hierarchy

Abstract

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