The N-soliton solution of the Degasperis-Procesi equation
arXiv:nlin/0511029 · doi:10.1088/0266-5611/21/5/004
Abstract
This paper extends the results of the previous paper designated I hereafter in which the one- and two-soiton solutions of the Degasperis-Procesi(DP) equation were obtained and their peakon limit was considered. Here, we present the general N-soliton solution of the DP equation and investigate its property. We show that it has a novel structure expressed by a parametric representation in terms of the BKP tau-functions. A purely algebraic proof of the solution is given by establishing various identities among the tau-functions. The large time asymptotic of the solution recovers the formula for the phase shift which was derived in I by a different method. Finally, the structure of the N-soliton solution is discussed in comparison with that of the Camassa-Holm shallow water wave equation.
To appear in Inverse Problems. Related paper: Y. Matsuno, Inverse Problems 21(2005)1553-1570
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- An integrable semi-discrete Degasperis-Procesi equation
- Unique Continuation Properties for solutions to the Camassa-Holm equation and other non-local equations
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