Riemann-Hilbert approach to the algebro-geometric solution of the modified Camassa-Holm equation with linear dispersion term

This paper aims at providing an exact algebro-geometric solution of the modified Camassa-Holm (mCH) equation derived from hyperelliptic curves in 4 ( p + q ) − 1 4(p+q)-1 genus. To achieve this goal, we construct the Riemann-Hilbert problems cosponsoring to the mCH equation, which can be solved exactly by the Baker-Akhiezer function. Then the precise expression of the algebro-geometric solution of the mCH equation can be obtained through reconstructed formula.