On application of Liouville type equations to constructing Bäcklund transformations

Dmitry Demskoi

doi:10.2991/jnmp.2007.14.1.11

On application of Liouville type equations to constructing Bäcklund transformations

Dmitry Demskoi

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

5 Citations (Scopus)

Abstract

It is shown how pseudoconstants of the Liouville-type equations can be exploited as a tool for construction of the Bäcklund transformations. Several new examples of such transformations are found. In particular we obtained the Bäcklund transformations for a pair of three-component analogs of the dispersive water wave system, and autoBäcklund transformations for coupled three-component KdV-type systems.

Original language	English
Pages (from-to)	147-156
Number of pages	10
Journal	Journal of Nonlinear Mathematical Physics
Volume	14
Issue number	1
DOIs	https://doi.org/10.2991/jnmp.2007.14.1.11
Publication status	Published - 2007

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10.2991/jnmp.2007.14.1.11

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abstract = "It is shown how pseudoconstants of the Liouville-type equations can be exploited as a tool for construction of the B{\"a}cklund transformations. Several new examples of such transformations are found. In particular we obtained the B{\"a}cklund transformations for a pair of three-component analogs of the dispersive water wave system, and autoB{\"a}cklund transformations for coupled three-component KdV-type systems.",

keywords = "B{\"a} cklund transformation, Integral, Miura transformation",

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N2 - It is shown how pseudoconstants of the Liouville-type equations can be exploited as a tool for construction of the Bäcklund transformations. Several new examples of such transformations are found. In particular we obtained the Bäcklund transformations for a pair of three-component analogs of the dispersive water wave system, and autoBäcklund transformations for coupled three-component KdV-type systems.

AB - It is shown how pseudoconstants of the Liouville-type equations can be exploited as a tool for construction of the Bäcklund transformations. Several new examples of such transformations are found. In particular we obtained the Bäcklund transformations for a pair of three-component analogs of the dispersive water wave system, and autoBäcklund transformations for coupled three-component KdV-type systems.

KW - Bä cklund transformation

KW - Integral

KW - Miura transformation

U2 - 10.2991/jnmp.2007.14.1.11

DO - 10.2991/jnmp.2007.14.1.11

M3 - Article

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VL - 14

SP - 147

EP - 156

JO - Journal of Nonlinear Mathematical Physics

JF - Journal of Nonlinear Mathematical Physics

IS - 1

ER -

On application of Liouville type equations to constructing Bäcklund transformations

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