An integrable semi-discrete Degasperis–Procesi equation. (19th April 2017)

• Record Type: Journal Article
• Authors: Feng, Bao-Feng; Maruno, Ken-ichi; Ohta, Yasuhiro
• Is Part Of: Nonlinearity. Volume 30:Number 6(2017:Jun.)
• Page Start: 2246
• Page End: 2267
• Publication Date: 2017-04-19
• Subjects: CKP hierarchy -- tau-functions -- bilinear equations -- semi-discrete Degasperis–Procesi equation; 35Q51 (primary) -- 37K40 -- 35L05 -- 34K31; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aa67fc
• Languages: English
• ISSNs: 0951-7715

Abstract

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.