An integrable hierarchy and Darboux transformations, bilinear Bäcklund transformations of a reduced equation

Yufeng Zhang; Zhong Han; Hon Wah Tam

doi:10.1016/j.amc.2012.11.086

An integrable hierarchy and Darboux transformations, bilinear Bäcklund transformations of a reduced equation

Yufeng Zhang^*, Zhong Han, Hon Wah Tam

^*Corresponding author for this work

Department of Computer Science

Research output: Contribution to journal › Journal article › peer-review

15 Citations (Scopus)

Abstract

A new integrable hierarchy of evolution equations is obtained by making use of a Lie algebra and Tu-Ma scheme, from which a new generalized Broer-Kaup (gBK) equation is produced. Then two kinds of Darboux transformations, the bilinear presentation, the bilinear Bäcklund transformation and the new Lax pair of the gBK equation are generated, respectively, by employing the Bell polynomials.

Original language	English
Pages (from-to)	5837-5848
Number of pages	12
Journal	Applied Mathematics and Computation
Volume	219
Issue number	11
DOIs	https://doi.org/10.1016/j.amc.2012.11.086
Publication status	Published - 1 Feb 2013

Scopus Subject Areas

Computational Mathematics
Applied Mathematics

User-Defined Keywords

Bäcklund transformation
Bell polynomials
Integrable hierarchy

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10.1016/j.amc.2012.11.086

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title = "An integrable hierarchy and Darboux transformations, bilinear B{\"a}cklund transformations of a reduced equation",

abstract = "A new integrable hierarchy of evolution equations is obtained by making use of a Lie algebra and Tu-Ma scheme, from which a new generalized Broer-Kaup (gBK) equation is produced. Then two kinds of Darboux transformations, the bilinear presentation, the bilinear B{\"a}cklund transformation and the new Lax pair of the gBK equation are generated, respectively, by employing the Bell polynomials.",

keywords = "B{\"a}cklund transformation, Bell polynomials, Integrable hierarchy",

author = "Yufeng Zhang and Zhong Han and Tam, {Hon Wah}",

note = "Funding Information: This work was supported by the Fundamental Research Funds for the Central Universities (2012 LWB51).",

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doi = "10.1016/j.amc.2012.11.086",

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T1 - An integrable hierarchy and Darboux transformations, bilinear Bäcklund transformations of a reduced equation

AU - Zhang, Yufeng

AU - Han, Zhong

AU - Tam, Hon Wah

N1 - Funding Information: This work was supported by the Fundamental Research Funds for the Central Universities (2012 LWB51).

PY - 2013/2/1

Y1 - 2013/2/1

N2 - A new integrable hierarchy of evolution equations is obtained by making use of a Lie algebra and Tu-Ma scheme, from which a new generalized Broer-Kaup (gBK) equation is produced. Then two kinds of Darboux transformations, the bilinear presentation, the bilinear Bäcklund transformation and the new Lax pair of the gBK equation are generated, respectively, by employing the Bell polynomials.

AB - A new integrable hierarchy of evolution equations is obtained by making use of a Lie algebra and Tu-Ma scheme, from which a new generalized Broer-Kaup (gBK) equation is produced. Then two kinds of Darboux transformations, the bilinear presentation, the bilinear Bäcklund transformation and the new Lax pair of the gBK equation are generated, respectively, by employing the Bell polynomials.

KW - Bäcklund transformation

KW - Bell polynomials

KW - Integrable hierarchy

UR - http://www.scopus.com/inward/record.url?scp=84872810702&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2012.11.086

DO - 10.1016/j.amc.2012.11.086

M3 - Journal article

AN - SCOPUS:84872810702

SN - 0096-3003

VL - 219

SP - 5837

EP - 5848

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 11

ER -

An integrable hierarchy and Darboux transformations, bilinear Bäcklund transformations of a reduced equation

Abstract

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