Annals of Mathematical Sciences and Applications

Volume 2 (2017)

Number 2

Guest Editors: Tai-Chia Lin (National Taiwan University), Wen-Wei Lin (National Chiao Tung University), Tony Wen-Hann Sheu (National Taiwan University), Weichung Wang (National Taiwan University), Chih-wen Weng (National Chiao Tung University), and Salil Vadhan (Harvard University).

The Degasperis–Procesi equation, its short wave model and the CKP hierarchy

Pages: 285 – 316



Bao-Feng Feng (School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, Texas, U.S.A.)

Ken-Ichi Maruno (Department of Applied Mathematics, Waseda University, Tokyo, Japan)

Yasuhiro Ohta (Department of Mathematics, Kobe University, Rokko, Kobe, Japan)


In the present paper, we show that the Degasperis–Procesi equation and its short-wave model (also known as the reduced-Ostrovsky equation or the Vakhnenko equation) are reductions of $C_{\infty}$-type two-dimensional Toda-lattices. Bilinear equations are presented to give rise the DP equation and its short-wave model directly through hodograph transformations. As a by-product, the parametric forms of $N$-soliton solutions are given in terms of pfaffians. One and two-soliton solutions to the DP equation are especially investigated to reveal their properties.

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Paper received on 2 October 2016.