Grammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation

Ya Ning Tang; Wen Xiu Ma; Wei Xu

doi:10.1088/1674-1056/21/7/070212

Grammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation

Ya Ning Tang, Wen Xiu Ma, Wei Xu

School of Mathematics and Statistics

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

55 Scopus citations

Abstract

Based on the Grammian and Pfaffian derivative formulae, Grammian and Pfaffian solutions are obtained for a (3+1)-dimensional generalized shallow water equation in the Hirota bilinear form. Moreover, a Pfaffian extension is made for the equation by means of the Pfaffianization procedure, the Wronski-type and Gramm-type Pfaffian solutions of the resulting coupled system are presented.

Original language	English
Article number	070212
Journal	Chinese Physics B
Volume	21
Issue number	7
DOIs	https://doi.org/10.1088/1674-1056/21/7/070212
State	Published - Jul 2012

Keywords

Grammian and Pfaffian solutions
Hirota bilinear form
Wronski-type and Gramm-type Pfaffian solutions

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10.1088/1674-1056/21/7/070212

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title = "Grammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation",

abstract = "Based on the Grammian and Pfaffian derivative formulae, Grammian and Pfaffian solutions are obtained for a (3+1)-dimensional generalized shallow water equation in the Hirota bilinear form. Moreover, a Pfaffian extension is made for the equation by means of the Pfaffianization procedure, the Wronski-type and Gramm-type Pfaffian solutions of the resulting coupled system are presented.",

keywords = "Grammian and Pfaffian solutions, Hirota bilinear form, Wronski-type and Gramm-type Pfaffian solutions",

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T1 - Grammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation

AU - Tang, Ya Ning

AU - Ma, Wen Xiu

AU - Xu, Wei

PY - 2012/7

Y1 - 2012/7

N2 - Based on the Grammian and Pfaffian derivative formulae, Grammian and Pfaffian solutions are obtained for a (3+1)-dimensional generalized shallow water equation in the Hirota bilinear form. Moreover, a Pfaffian extension is made for the equation by means of the Pfaffianization procedure, the Wronski-type and Gramm-type Pfaffian solutions of the resulting coupled system are presented.

AB - Based on the Grammian and Pfaffian derivative formulae, Grammian and Pfaffian solutions are obtained for a (3+1)-dimensional generalized shallow water equation in the Hirota bilinear form. Moreover, a Pfaffian extension is made for the equation by means of the Pfaffianization procedure, the Wronski-type and Gramm-type Pfaffian solutions of the resulting coupled system are presented.

KW - Grammian and Pfaffian solutions

KW - Hirota bilinear form

KW - Wronski-type and Gramm-type Pfaffian solutions

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U2 - 10.1088/1674-1056/21/7/070212

DO - 10.1088/1674-1056/21/7/070212

M3 - 文章

AN - SCOPUS:84864265198

SN - 1674-1056

VL - 21

JO - Chinese Physics B

JF - Chinese Physics B

IS - 7

M1 - 070212

ER -

Grammian and Pfaffian solutions as well as Pfaffianization for a (3+1)-dimensional generalized shallow water equation

Abstract

Keywords

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