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Inverse Scattering Transform For The Degasperis–Procesi Equation, Adrian Constantin, Rossen Ivanov, Jonatan Lenells
Inverse Scattering Transform For The Degasperis–Procesi Equation, Adrian Constantin, Rossen Ivanov, Jonatan Lenells
Articles
We develop the Inverse Scattering Transform (IST) method for the Degasperis- Procesi equation. The spectral problem is an 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.