A Riemann-Hilbert approach to the modified Camassa-Holm equation with step-like boundary conditions

The paper aims at developing the Riemann-Hilbert (RH) approach for the modified Camassa-Holm (mCH) equation on the line with non-zero boundary conditions, in the case when the solution is assumed to approach two different constants at different sides of the line. We present detailed properties of spectral functions associated with the initial data for the Cauchy problem for the mCH equation and obtain a representation for the solution of this problem in terms of the solution of an associated RH problem.

Automated summary

This paper aims to develop the Riemann-Hilbert approach for the modified Camassa-Holm equation with non-zero boundary conditions. It presents detailed properties of spectral functions associated with the initial data and obtains a representation for the solution of the Cauchy problem in terms of an associated RH problem.