The Modified Camassa–Holm Equation on the Half Line: A Riemann–Hilbert Approach
Iryna Karpenko, Dmitry Shepelsky
Source abstract
ABSTRACT We consider the initial‐boundary value (IBV) problem for the modified Camassa–Holm (mCH) equation on the half‐line . We provide a characterization of the solution of the IBV problem in terms of the solution of a matrix Riemann–Hilbert (RH) factorization problem in the complex plane of the spectral parameter. The data of this RH problem are determined in terms of spectral functions associated with the initial and boundary values of the solution, whose compatibility is characterized in spectral terms.
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