Inverse scattering transform for the Degasperis–Procesi equation

By Adrian Constantin, Rossen I. Ivanov, Jonatan Lenells. 2010

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We develop the inverse scattering transform (IST) method for the Degasperis–Procesi equation. The spectral problem is an 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.

Subfields: Applied Mathematics, Mathematical Physics

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