On the τ-functions of the Degasperis–Procesi equation

Abstract

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