Generalized mkdv equation, liouville equation,sine-gordon equation and sinh-gordon equation as well as a formal bäcklund transformation

Yufeng Zhang; Honwah Tam; Jing Zhao

doi:10.1142/S0217979211101387

Generalized mkdv equation, liouville equation,sine-gordon equation and sinh-gordon equation as well as a formal bäcklund transformation

Yufeng Zhang^*, Honwah Tam, Jing Zhao

^*Corresponding author for this work

Department of Computer Science

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

2 Citations (Scopus)

Abstract

A Lie algebra which consists of linear combinations of one basis of the Lie algebra A₁ is presented for which an isospectral Lax pair is exhibited. By using the zero curvature equation, the generalized mKdV equation, Liouville equation and sine-Gordon equation, sinh-Gordon equation are generated via polynomial expansions. Finally, we investigate a kind of formal Bäcklund transformation for the generalized sine-Gordon equation. The explicit Bäcklund transformation of the standard sine-Gordon equation is presented. The other equations given in the paper are obtained similarly.

Original language	English
Pages (from-to)	2449-2460
Number of pages	12
Journal	International Journal of Modern Physics B
Volume	25
Issue number	18
DOIs	https://doi.org/10.1142/S0217979211101387
Publication status	Published - 20 Jul 2011

User-Defined Keywords

Bäcklund transformation
Lie algebra
Liouville equation
mKdV equation
sine-Gordon equation
sinh-Gordon equation

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10.1142/S0217979211101387

Cite this

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title = "Generalized mkdv equation, liouville equation,sine-gordon equation and sinh-gordon equation as well as a formal b{\"a}cklund transformation",

abstract = "A Lie algebra which consists of linear combinations of one basis of the Lie algebra A1 is presented for which an isospectral Lax pair is exhibited. By using the zero curvature equation, the generalized mKdV equation, Liouville equation and sine-Gordon equation, sinh-Gordon equation are generated via polynomial expansions. Finally, we investigate a kind of formal B{\"a}cklund transformation for the generalized sine-Gordon equation. The explicit B{\"a}cklund transformation of the standard sine-Gordon equation is presented. The other equations given in the paper are obtained similarly.",

keywords = "B{\"a}cklund transformation, Lie algebra, Liouville equation, mKdV equation, sine-Gordon equation, sinh-Gordon equation",

author = "Yufeng Zhang and Honwah Tam and Jing Zhao",

note = "Funding Information: The work was supported by Hong Kong RGC Grant No. HKBU 2022007 and Natural Science Foundation of Shandong Province (ZR2009AL021).",

year = "2011",

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language = "English",

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T1 - Generalized mkdv equation, liouville equation,sine-gordon equation and sinh-gordon equation as well as a formal bäcklund transformation

AU - Zhang, Yufeng

AU - Tam, Honwah

AU - Zhao, Jing

N1 - Funding Information: The work was supported by Hong Kong RGC Grant No. HKBU 2022007 and Natural Science Foundation of Shandong Province (ZR2009AL021).

PY - 2011/7/20

Y1 - 2011/7/20

N2 - A Lie algebra which consists of linear combinations of one basis of the Lie algebra A1 is presented for which an isospectral Lax pair is exhibited. By using the zero curvature equation, the generalized mKdV equation, Liouville equation and sine-Gordon equation, sinh-Gordon equation are generated via polynomial expansions. Finally, we investigate a kind of formal Bäcklund transformation for the generalized sine-Gordon equation. The explicit Bäcklund transformation of the standard sine-Gordon equation is presented. The other equations given in the paper are obtained similarly.

AB - A Lie algebra which consists of linear combinations of one basis of the Lie algebra A1 is presented for which an isospectral Lax pair is exhibited. By using the zero curvature equation, the generalized mKdV equation, Liouville equation and sine-Gordon equation, sinh-Gordon equation are generated via polynomial expansions. Finally, we investigate a kind of formal Bäcklund transformation for the generalized sine-Gordon equation. The explicit Bäcklund transformation of the standard sine-Gordon equation is presented. The other equations given in the paper are obtained similarly.

KW - Bäcklund transformation

KW - Lie algebra

KW - Liouville equation

KW - mKdV equation

KW - sine-Gordon equation

KW - sinh-Gordon equation

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DO - 10.1142/S0217979211101387

M3 - Journal article

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SN - 0217-9792

VL - 25

SP - 2449

EP - 2460

JO - International Journal of Modern Physics B

JF - International Journal of Modern Physics B

IS - 18

ER -

Generalized mkdv equation, liouville equation,sine-gordon equation and sinh-gordon equation as well as a formal bäcklund transformation

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