Algebro-geometric integration of the Hirota equation and the Riemann–Hilbert problem

Abstract

Based on the Riemann–Hilbert method, the Riemann theta function representations for algebro-geometric solutions of the Hirota equation are derived. It is shown that the Baker–Akhiezer function of the Hirota equation can be described by solvable matrix Riemann–Hilbert problems on complex plane. The procedure avoids the use of Dubrovin's equations and Jacobi inverse problem.