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Inverse Scattering Transform for the Degasperis-Procesi Equation

Published 21 May 2012 in nlin.SI and nlin.PS | (1205.4754v1)

Abstract: We develop the Inverse Scattering Transform (IST) method for the Degasperis-Procesi equation. The spectral problem is an $\mathfrak{sl}(3)$ Zakharov-Shabat problem with constant boundary conditions and finite reduction group. The basic aspects of the IST such as the construction of fundamental analytic solutions, the formulation of a Riemann-Hilbert problem, and the implementation of the dressing method are presented.

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