Wronskian and Grammian solutions to a (3 + 1)-dimensional generalized KP equation

Wen Xiu Ma; Alrazi Abdeljabbar; Magdy Gamil Asaad

doi:10.1016/j.amc.2011.04.077

Wronskian and Grammian solutions to a (3 + 1)-dimensional generalized KP equation

Wen Xiu Ma
, Alrazi Abdeljabbar
, Magdy Gamil Asaad

Mathematics

University of South Florida, Tampa

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

132 Scopus citations

Abstract

Wronskian and Grammian formulations are established for a (3 + 1)-dimensional generalized KP equation, based on the Plücker relation and the Jacobi identity for determinants. Generating functions for matrix entries satisfy a linear system of partial differential equations involving a free parameter. Examples of Wronskian and Grammian solutions are computed and a few particular solutions are plotted.

Original language	British English
Pages (from-to)	10016-10023
Number of pages	8
Journal	Applied Mathematics and Computation
Volume	217
Issue number	24
DOIs	https://doi.org/10.1016/j.amc.2011.04.077
State	Published - 15 Aug 2011

Keywords

Grammian solution
Hirota bilinear form
Wronskian solution

Access to Document

10.1016/j.amc.2011.04.077

OpenUrl availability

Full text

Cite this

@article{e5cb26ea33d84dfd8ecf1a352a724bcb,

title = "Wronskian and Grammian solutions to a (3 + 1)-dimensional generalized KP equation",

abstract = "Wronskian and Grammian formulations are established for a (3 + 1)-dimensional generalized KP equation, based on the Pl{\"u}cker relation and the Jacobi identity for determinants. Generating functions for matrix entries satisfy a linear system of partial differential equations involving a free parameter. Examples of Wronskian and Grammian solutions are computed and a few particular solutions are plotted.",

keywords = "Grammian solution, Hirota bilinear form, Wronskian solution",

author = "Ma, \{Wen Xiu\} and Alrazi Abdeljabbar and Asaad, \{Magdy Gamil\}",

note = "Funding Information: The work was supported in part by the State Administration of Foreign Experts Affairs of China , the National Natural Science Foundation of China (Nos. 10831003 , 61072147 and 11071159 ), Chunhui Plan of the Ministry of Education of China , Zhejiang Innovation Project (Grant No. T200905 ), the Natural Science Foundation of Shanghai and the Shanghai Leading Academic Discipline Project (No. J50101 ). The authors also would like to thank Tian Dong, Kathleen Guy, Netra Khanal, Morgan McAnally, Yaning Tang, Junyi Tu, Tiecheng Xia and Yi Zhang for their interests and valuable discussions.",

year = "2011",

month = aug,

day = "15",

doi = "10.1016/j.amc.2011.04.077",

language = "British English",

volume = "217",

pages = "10016--10023",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier Inc.",

number = "24",

}

TY - JOUR

T1 - Wronskian and Grammian solutions to a (3 + 1)-dimensional generalized KP equation

AU - Ma, Wen Xiu

AU - Abdeljabbar, Alrazi

AU - Asaad, Magdy Gamil

N1 - Funding Information: The work was supported in part by the State Administration of Foreign Experts Affairs of China , the National Natural Science Foundation of China (Nos. 10831003 , 61072147 and 11071159 ), Chunhui Plan of the Ministry of Education of China , Zhejiang Innovation Project (Grant No. T200905 ), the Natural Science Foundation of Shanghai and the Shanghai Leading Academic Discipline Project (No. J50101 ). The authors also would like to thank Tian Dong, Kathleen Guy, Netra Khanal, Morgan McAnally, Yaning Tang, Junyi Tu, Tiecheng Xia and Yi Zhang for their interests and valuable discussions.

PY - 2011/8/15

Y1 - 2011/8/15

N2 - Wronskian and Grammian formulations are established for a (3 + 1)-dimensional generalized KP equation, based on the Plücker relation and the Jacobi identity for determinants. Generating functions for matrix entries satisfy a linear system of partial differential equations involving a free parameter. Examples of Wronskian and Grammian solutions are computed and a few particular solutions are plotted.

AB - Wronskian and Grammian formulations are established for a (3 + 1)-dimensional generalized KP equation, based on the Plücker relation and the Jacobi identity for determinants. Generating functions for matrix entries satisfy a linear system of partial differential equations involving a free parameter. Examples of Wronskian and Grammian solutions are computed and a few particular solutions are plotted.

KW - Grammian solution

KW - Hirota bilinear form

KW - Wronskian solution

UR - https://www.scopus.com/pages/publications/79959236580

U2 - 10.1016/j.amc.2011.04.077

DO - 10.1016/j.amc.2011.04.077

M3 - Article

AN - SCOPUS:79959236580

SN - 0096-3003

VL - 217

SP - 10016

EP - 10023

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 24

ER -

Wronskian and Grammian solutions to a (3 + 1)-dimensional generalized KP equation

Abstract

Keywords

Access to Document

OpenUrl availability

Other files and links

Fingerprint

Cite this