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October 13, 2025Open Access

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

EFEngui FanZhejiang Normal University GLGaozhan LiTsinghua University YYYiling YangChongqing University

Key Points

The study provides an exact algebro-geometric solution to the modified Camassa-Holm equation, expanding on existing theories.
Key findings leverage Riemann-Hilbert problems to construct solutions using Baker-Akhiezer functions effectively.
The solution is tied to hyperelliptic curves of the mCH equation potentially revolutionizing dispersion analysis.
Constructing the algebro-geometric solution through explicit formulas illustrates the interplay between geometry and analysis.

Abstract

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 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.

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