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This paper extends the results of the previous paper designated I hereafterin which the one- and two-soiton solutions of the Degasperis-Procesi(DP)equation were obtained and their peakon limit was considered. Here, we presentthe general N-soliton solution of the DP equation and investigate its property.We show that it has a novel structure expressed by a parametric representationin terms of the BKP tau-functions. A purely algebraic proof of the solution isgiven by establishing various identities among the tau-functions. The largetime asymptotic of the solution recovers the formula for the phase shift whichwas derived in I by a different method. Finally, the structure of the N-solitonsolution is discussed in comparison with that of the Camassa-Holm shallow waterwave equation.Comment: To appear in Inverse Problems. Related paper: Y. Matsuno, Inverse  Problems 21(2005)1553-157

Multisoliton solutions of the Degasperis–Procesi equation and their peakon limit