Painlevé analysis and new analytic solutions for (1+1)-dimensional higher-order Broer-Kaup system with symbolic computation

Xiao Nan Li; Guang Mei Wei; Yu Ping Liu; Yue Qian Liang; Xiang Hua Meng

doi:10.1142/S0217979214500672

Painlevé analysis and new analytic solutions for (1+1)-dimensional higher-order Broer-Kaup system with symbolic computation

Xiao Nan Li
, Guang Mei Wei
, Yu Ping Liu
, Yue Qian Liang
, Xiang Hua Meng

School of Mathematical Sciences

Beihang University
Beijing Information Science & Technology University

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

4 Scopus citations

Abstract

The (1+1)-dimensional higher-order Broer-Kaup (HBK) system is investigated in this paper. Painlevé test shows that there are two solution branches, one of which has the resonance -2. And an auto-Bäcklund transformation is obtained by the truncated Painlevé expansion. The new analytic solutions are presented by means of the auto-Bäcklund transformation, including the periodic and soliton-like solutions. Similarity reductions for the HBK system are given out to two ordinary differential equations (ODEs) through CK direct method.

Original language	English
Article number	1450067
Journal	International Journal of Modern Physics B
Volume	28
Issue number	14
DOIs	https://doi.org/10.1142/S0217979214500672
State	Published - 10 Jun 2014

Keywords

Broer-Kaup system
Painlevé analysis
analytic solution
auto-Bäcklund transformation
similarity reduction
symbolic computation

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10.1142/S0217979214500672

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title = "Painlev{\'e} analysis and new analytic solutions for (1+1)-dimensional higher-order Broer-Kaup system with symbolic computation",

abstract = "The (1+1)-dimensional higher-order Broer-Kaup (HBK) system is investigated in this paper. Painlev{\'e} test shows that there are two solution branches, one of which has the resonance -2. And an auto-B{\"a}cklund transformation is obtained by the truncated Painlev{\'e} expansion. The new analytic solutions are presented by means of the auto-B{\"a}cklund transformation, including the periodic and soliton-like solutions. Similarity reductions for the HBK system are given out to two ordinary differential equations (ODEs) through CK direct method.",

keywords = "Broer-Kaup system, Painlev{\'e} analysis, analytic solution, auto-B{\"a}cklund transformation, similarity reduction, symbolic computation",

author = "Li, \{Xiao Nan\} and Wei, \{Guang Mei\} and Liu, \{Yu Ping\} and Liang, \{Yue Qian\} and Meng, \{Xiang Hua\}",

year = "2014",

month = jun,

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doi = "10.1142/S0217979214500672",

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journal = "International Journal of Modern Physics B",

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T1 - Painlevé analysis and new analytic solutions for (1+1)-dimensional higher-order Broer-Kaup system with symbolic computation

AU - Li, Xiao Nan

AU - Wei, Guang Mei

AU - Liu, Yu Ping

AU - Liang, Yue Qian

AU - Meng, Xiang Hua

PY - 2014/6/10

Y1 - 2014/6/10

N2 - The (1+1)-dimensional higher-order Broer-Kaup (HBK) system is investigated in this paper. Painlevé test shows that there are two solution branches, one of which has the resonance -2. And an auto-Bäcklund transformation is obtained by the truncated Painlevé expansion. The new analytic solutions are presented by means of the auto-Bäcklund transformation, including the periodic and soliton-like solutions. Similarity reductions for the HBK system are given out to two ordinary differential equations (ODEs) through CK direct method.

AB - The (1+1)-dimensional higher-order Broer-Kaup (HBK) system is investigated in this paper. Painlevé test shows that there are two solution branches, one of which has the resonance -2. And an auto-Bäcklund transformation is obtained by the truncated Painlevé expansion. The new analytic solutions are presented by means of the auto-Bäcklund transformation, including the periodic and soliton-like solutions. Similarity reductions for the HBK system are given out to two ordinary differential equations (ODEs) through CK direct method.

KW - Broer-Kaup system

KW - Painlevé analysis

KW - analytic solution

KW - auto-Bäcklund transformation

KW - similarity reduction

KW - symbolic computation

UR - https://www.scopus.com/pages/publications/84899633867

U2 - 10.1142/S0217979214500672

DO - 10.1142/S0217979214500672

M3 - 文章

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SN - 0217-9792

VL - 28

JO - International Journal of Modern Physics B

JF - International Journal of Modern Physics B

IS - 14

M1 - 1450067

ER -

Painlevé analysis and new analytic solutions for (1+1)-dimensional higher-order Broer-Kaup system with symbolic computation

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Keywords

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