On the tau-functions of the Degasperis-Procesi equation

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.

27 pages, 4 figures, Journal of Physics A: Mathematical and Theoretical, to be published

References in corpus (4)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Integrable discretizations of the short pulse equation
• An integrable semi-discretization of the Camassa-Holm equation and its determinant solution
• Tzitzeica solitons vs. relativistic Calogero-Moser 3-body clusters

Cited by in corpus (4)

• Degasperis-Procesi peakon dynamical system and finite Toda lattice of CKP type
• Integrable semi-discretizations of the reduced Ostrovsky equation
• A view of the peakon world through the lens of approximation theory
• Unfamiliar Aspects of Bäcklund Transformations and an Associated Degasperis-Procesi Equation