1207.5347 (Bao-Feng Feng et al.)

On the tau-functions of the Degasperis-Procesi equation    [PDF]

Bao-Feng Feng, Ken-ichi Maruno, Yasuhiro Ohta

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-function of the DP equation are obtained from the pseudo 3-reduction of the $C_{\infty}$ two-dimensional Toda system.

View original: http://arxiv.org/abs/1207.5347