Inverse Scattering Transform for the Degasperis-Procesi Equation

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

References in corpus (8)

• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• Inverse Scattering Transform for the Camassa-Holm equation
• Water Waves and Integrability
• A New Integrable Equation with Peakon Solutions
• On the Caudrey-Beals-Coifman System and the Gauge Group Action
• Basic aspects of soliton theory
• New Integrable Multi-Component NLS Type Equations on Symmetric Spaces: Z_4 and Z_6 Reductions
• On the Multi-Component Nonlinear Schrödinger Equation with Constant Boundary Conditions

Cited by in corpus (1)

• Multi loop soliton solutions and their interactions in the Degasperis-Procesi equation