Nonlocal symmetries and explicit solutions of the Boussinesq equation

Xiangpeng Xin; Junchao Chen; Yong Chen

doi:10.1007/s11401-014-0868-2

Nonlocal symmetries and explicit solutions of the Boussinesq equation

Xiangpeng Xin, Junchao Chen, Yong Chen

School of Mathematical Sciences

East China Normal University

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

12 Scopus citations

Abstract

The nonlocal symmetry of the Boussinesq equation is obtained from the known Lax pair. The explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetry. Some other types of solutions, such as rational solutions and error function solutions, are given by using the fourth Painlevé equation with special values of the parameters. For some interesting solutions, the figures are given out to show their properties.

Original language	English
Pages (from-to)	841-856
Number of pages	16
Journal	Chinese Annals of Mathematics. Series B
Volume	35
Issue number	6
DOIs	https://doi.org/10.1007/s11401-014-0868-2
State	Published - Nov 2014

Keywords

Explicit solution
Lax pair
Nonlocal symmetry
Prolonged system

Access to Document

10.1007/s11401-014-0868-2

Cite this

@article{9ed6b8b1f2dd45e2930b2c4bad64006f,

title = "Nonlocal symmetries and explicit solutions of the Boussinesq equation",

abstract = "The nonlocal symmetry of the Boussinesq equation is obtained from the known Lax pair. The explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetry. Some other types of solutions, such as rational solutions and error function solutions, are given by using the fourth Painlev{\'e} equation with special values of the parameters. For some interesting solutions, the figures are given out to show their properties.",

keywords = "Explicit solution, Lax pair, Nonlocal symmetry, Prolonged system",

author = "Xiangpeng Xin and Junchao Chen and Yong Chen",

note = "Publisher Copyright: {\textcopyright} 2014, Fudan University and Springer-Verlag Berlin Heidelberg.",

year = "2014",

month = nov,

doi = "10.1007/s11401-014-0868-2",

language = "英语",

volume = "35",

pages = "841--856",

journal = "Chinese Annals of Mathematics. Series B",

issn = "0252-9599",

publisher = "Springer Verlag",

number = "6",

}

TY - JOUR

T1 - Nonlocal symmetries and explicit solutions of the Boussinesq equation

AU - Xin, Xiangpeng

AU - Chen, Junchao

AU - Chen, Yong

PY - 2014/11

Y1 - 2014/11

N2 - The nonlocal symmetry of the Boussinesq equation is obtained from the known Lax pair. The explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetry. Some other types of solutions, such as rational solutions and error function solutions, are given by using the fourth Painlevé equation with special values of the parameters. For some interesting solutions, the figures are given out to show their properties.

AB - The nonlocal symmetry of the Boussinesq equation is obtained from the known Lax pair. The explicit analytic interaction solutions between solitary waves and cnoidal waves are obtained through the localization procedure of nonlocal symmetry. Some other types of solutions, such as rational solutions and error function solutions, are given by using the fourth Painlevé equation with special values of the parameters. For some interesting solutions, the figures are given out to show their properties.

KW - Explicit solution

KW - Lax pair

KW - Nonlocal symmetry

KW - Prolonged system

UR - https://www.scopus.com/pages/publications/84919949744

U2 - 10.1007/s11401-014-0868-2

DO - 10.1007/s11401-014-0868-2

M3 - 文章

AN - SCOPUS:84919949744

SN - 0252-9599

VL - 35

SP - 841

EP - 856

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 6

ER -

Nonlocal symmetries and explicit solutions of the Boussinesq equation

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this