Inverse scattering transform for the Degasperis-Procesi equation: a Riemann-Hilbert approach

Details Inverse scattering transform for the Degasperis-Procesi equation: a Riemann-Hilbert approach Inverse scattering transform for the Degasperis-Procesi equation: a Riemann-Hilbert approach

2011-07-29

arxiv.org/abs/1107.5995v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

Scientific paper

We present the inverse scattering transform approach to the Cauchy problem on the line for the Degasperis-Procesi equation $u_{txx}-2u_x+2u_xu_{xx}+uu_{xxx}=0$ in the form of an associated Riemann-Hilbert problem. This approach allows us to give a representation of the solution to the Cauchy problem, which can be efficiently used in studying its long-time behavior.

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