Inverse Scattering Transform for the Degasperis-Procesi Equation
arXiv:1205.4754 · doi:10.1088/0951-7715/23/10/012
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.
18 pages, 1 figure