On the (2 + 1)-dimensional Gardner equation: Determinant solutions and pfaffianization

Guo Fu Yu; Hon Wah Tam

doi:10.1016/j.jmaa.2006.08.021

On the (2 + 1)-dimensional Gardner equation: Determinant solutions and pfaffianization

Guo Fu Yu^*
, Hon Wah Tam

^*Corresponding author for this work

Department of Computer Science

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

29 Citations (Scopus)

Abstract

In this paper, we first present the Casorati and Grammian determinant solutions to the (2 + 1)-dimensional Gardner equation. Then, by using the pfaffianization procedure of Hirota and Ohta, a new integrable coupled system is generated from the Gardner equation. Moreover, Gramm-type pfaffian solutions to the pfaffianized system are proposed.

Original language	English
Pages (from-to)	989-1001
Number of pages	13
Journal	Journal of Mathematical Analysis and Applications
Volume	330
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2006.08.021
Publication status	Published - 15 Jun 2007

User-Defined Keywords

Casorati solution
Grammian determinant
Pfaffian
Soliton

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10.1016/j.jmaa.2006.08.021

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title = "On the (2 + 1)-dimensional Gardner equation: Determinant solutions and pfaffianization",

abstract = "In this paper, we first present the Casorati and Grammian determinant solutions to the (2 + 1)-dimensional Gardner equation. Then, by using the pfaffianization procedure of Hirota and Ohta, a new integrable coupled system is generated from the Gardner equation. Moreover, Gramm-type pfaffian solutions to the pfaffianized system are proposed.",

keywords = "Casorati solution, Grammian determinant, Pfaffian, Soliton",

author = "Yu, \{Guo Fu\} and Tam, \{Hon Wah\}",

note = "Funding Information: ✩ This work was supported by the National Natural Science Foundation of China (Grant No. 10471139), CAS President Grant, the Knowledge Innovation Program of Institute of Computational Mathematics, AMSS, Chinese Academy of Sciences, and Hong Kong Research Grant Council Grant Nos. HKBU2016/03P and HKBU2016/05P. * Corresponding author. E-mail address: [email protected] (G.-F. Yu).",

year = "2007",

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doi = "10.1016/j.jmaa.2006.08.021",

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T1 - On the (2 + 1)-dimensional Gardner equation

T2 - Determinant solutions and pfaffianization

AU - Yu, Guo Fu

AU - Tam, Hon Wah

N1 - Funding Information: ✩ This work was supported by the National Natural Science Foundation of China (Grant No. 10471139), CAS President Grant, the Knowledge Innovation Program of Institute of Computational Mathematics, AMSS, Chinese Academy of Sciences, and Hong Kong Research Grant Council Grant Nos. HKBU2016/03P and HKBU2016/05P. * Corresponding author. E-mail address: [email protected] (G.-F. Yu).

PY - 2007/6/15

Y1 - 2007/6/15

N2 - In this paper, we first present the Casorati and Grammian determinant solutions to the (2 + 1)-dimensional Gardner equation. Then, by using the pfaffianization procedure of Hirota and Ohta, a new integrable coupled system is generated from the Gardner equation. Moreover, Gramm-type pfaffian solutions to the pfaffianized system are proposed.

AB - In this paper, we first present the Casorati and Grammian determinant solutions to the (2 + 1)-dimensional Gardner equation. Then, by using the pfaffianization procedure of Hirota and Ohta, a new integrable coupled system is generated from the Gardner equation. Moreover, Gramm-type pfaffian solutions to the pfaffianized system are proposed.

KW - Casorati solution

KW - Grammian determinant

KW - Pfaffian

KW - Soliton

UR - https://www.scopus.com/pages/publications/33847618870

U2 - 10.1016/j.jmaa.2006.08.021

DO - 10.1016/j.jmaa.2006.08.021

M3 - Journal article

AN - SCOPUS:33847618870

SN - 0022-247X

VL - 330

SP - 989

EP - 1001

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

On the (2 + 1)-dimensional Gardner equation: Determinant solutions and pfaffianization

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