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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
DOI: https://dx.doi.org/10.4310/AMSA.2017.v2.n2.a4
Authors
Abstract
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.
Received 2 October 2016
Published 10 August 2017