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

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Cited by in corpus (17)

• Dressing Method for the Degasperis-Procesi Equation
• A Riemann-Hilbert Approach for the Novikov Equation
• Degasperis-Procesi peakon dynamical system and finite Toda lattice of CKP type
• Liouville Correspondences between Integrable Hierarchies
• Multi loop soliton solutions and their interactions in the Degasperis-Procesi equation
• Well-posedness of a highly nonlinear shallow water equation on the circle
• Camassa-Holm cuspons, solitons and their interactions via the dressing method
• NLS-type equations from quadratic pencil of Lax operators: negative flows
• Scattering for general-type Dirac systems on the semi-axis: reflection coefficients and Weyl functions
• On the Cauchy problem for a new integrable two-component system with peakon and weak kink solutions
• Integrable negative flows of the Heisenberg ferromagnet equation hierarchy
• Exponential decay and symmetry of solitary waves to the Degasperis-Procesi equation
• An integrable semi-discrete Degasperis-Procesi equation
• Riemann-Hilbert approach for a mixed coupled nonlinear Schrödinger system and its soliton solutions
• A unified inverse scattering transform and soliton solutions of the nonlocal modified KdV equation with non-zero boundary conditions
• Inverse scattering transform for the Tzitzéica equation
• Non-uniform dependence for the Novikov equation in Besov spaces