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Dressing method for the Degasperis-Procesi equation. (English) Zbl 1365.35134

The dressing method is used to construct explicit representations of the \(N\) solitons for the Degasperis-Procesi equation. It is based on the Lax pair representation of this completely integrable system and the associated inverse scattering transform [A. Constantin et al., Nonlinearity 23, No. 10, 2559–2575 (2010; Zbl 1211.37081)]. The \(N\) solitons have been constructed before by Hirota’s method [Y. Matsuno, Inverse Probl. 21, No. 5, 1553–1570 (2005; Zbl 1086.35095)]. The spectral construction completes the picture.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35C08 Soliton solutions
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
37K15 Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
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