A Riemann-Hilbert approach for the Degasperis-Procesi equation

We present an inverse scattering transform approach to the Cauchy problem on the line for the Degasperis–Procesi equation $u_t-u_{txx}+3\omega u_x+4uu_x=3u_xu_{xx}+uu_{xxx}$ 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.

💡 Research Summary

The paper develops a rigorous inverse scattering transform (IST) framework for the Cauchy problem of the Degasperis–Procesi (DP) equation on the real line, casting the problem into a matrix Riemann–Hilbert (RH) formulation. The DP equation,
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