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 › Article › peer-review

20 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

Scopus Subject Areas

Analysis
Applied Mathematics

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: gfyu@lsec.cc.ac.cn (G.-F. Yu).",

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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: gfyu@lsec.cc.ac.cn (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

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EP - 1001

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

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ER -

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

Abstract

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