An integrable semi-discrete Degasperis-Procesi equation

Bao Feng Feng; Ken Ichi Maruno; Yasuhiro Ohta

doi:10.1088/1361-6544/aa67fc

An integrable semi-discrete Degasperis-Procesi equation

Bao Feng Feng, Ken Ichi Maruno, Yasuhiro Ohta

School of Fundamental Science and Engineering

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

4 Citations (Scopus)

Abstract

Based on our previous work on the Degasperis-Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota's bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis-Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis-Procesi equation, and its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuum limit.

Original language	English
Pages (from-to)	2246-2267
Number of pages	22
Journal	Nonlinearity
Volume	30
Issue number	6
DOIs	https://doi.org/10.1088/1361-6544/aa67fc
Publication status	Published - 2017 Apr 19

Keywords

CKP hierarchy
bilinear equations
semi-discrete Degasperis-Procesi equation
tau-functions

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)
Applied Mathematics

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title = "An integrable semi-discrete Degasperis-Procesi equation",

abstract = "Based on our previous work on the Degasperis-Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota's bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis-Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis-Procesi equation, and its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuum limit.",

keywords = "CKP hierarchy, bilinear equations, semi-discrete Degasperis-Procesi equation, tau-functions",

author = "Feng, {Bao Feng} and Maruno, {Ken Ichi} and Yasuhiro Ohta",

note = "Funding Information: BF appreciated the partial support by the National Natural Science Foundation of China (No. 11428102). The work of KM is partially supported by JSPS Grant-in-Aid for Scientific Research (C-15K04909) and CREST, JST. The work of YO is partially supported by JSPS Grant-in-Aid for Scientific Research (B-24340029, C-15K04909) and for Challenging Exploratory Research (26610029). Publisher Copyright: {\textcopyright} 2017 IOP Publishing Ltd & London Mathematical Society.",

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doi = "10.1088/1361-6544/aa67fc",

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AU - Feng, Bao Feng

AU - Maruno, Ken Ichi

AU - Ohta, Yasuhiro

N1 - Funding Information: BF appreciated the partial support by the National Natural Science Foundation of China (No. 11428102). The work of KM is partially supported by JSPS Grant-in-Aid for Scientific Research (C-15K04909) and CREST, JST. The work of YO is partially supported by JSPS Grant-in-Aid for Scientific Research (B-24340029, C-15K04909) and for Challenging Exploratory Research (26610029). Publisher Copyright: © 2017 IOP Publishing Ltd & London Mathematical Society.

PY - 2017/4/19

Y1 - 2017/4/19

N2 - Based on our previous work on the Degasperis-Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota's bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis-Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis-Procesi equation, and its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuum limit.

AB - Based on our previous work on the Degasperis-Procesi equation (Feng et al J. Phys. A: Math. Theor. 46 045205) and the integrable semi-discrete analogue of its short wave limit (Feng et al J. Phys. A: Math. Theor. 48 135203), we derive an integrable semi-discrete Degasperis-Procesi equation by Hirota's bilinear method. Furthermore, N-soliton solution to the semi-discrete Degasperis-Procesi equation is constructed. It is shown that both the proposed semi-discrete Degasperis-Procesi equation, and its N-soliton solution converge to ones of the original Degasperis-Procesi equation in the continuum limit.

KW - CKP hierarchy

KW - bilinear equations

KW - semi-discrete Degasperis-Procesi equation

KW - tau-functions

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An integrable semi-discrete Degasperis-Procesi equation

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Keywords

ASJC Scopus subject areas

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