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arXiv · 1207.5347

On the tau-functions of the Degasperis-Procesi equation

Bao-Feng Feng·Ken-ichi Maruno·Yasuhiro Ohta
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Abstract

The DP equation is investigated from the point of view of determinant-pfaffian identities. The reciprocal link between the Degasperis-Procesi (DP) equation and the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system is used to construct the N-soliton solution of the DP equation. The N-soliton solution of the DP equation is presented in the form of pfaffian through a hodograph (reciprocal) transformation. The bilinear equations, the identities between determinants and pfaffians, and the $\tau$-functions of the DP equation are obtained from the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system.

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Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta. 2012-07-23. On the tau-functions of the Degasperis-Procesi equation. https://doi.org/10.1088/1751-8113/46/4/045205

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