New Construction of Algebro-Geometric Solutions to the Modified Kadomtsev-Petviashvili Hierarchy

We extend Gesztesy-Holden’s method to 2+1 dimensional case to obtain a unified construction to the algebro-geometric solutions of the whole modified Kadomtsev-Petviashvili (mKP) hierarchy. Our tools include the relations between solutions of the Gerdjikov-Ivanov (GI) and mKP hierarchy, the Baker-Akhiezer functions in 2+1 dimensions, a special function ${\psi }_1(P){\psi }_2(P^{\ast })$ on $X\times {\mathbb{R}}^3$ and Dubrovin-type equations for auxiliary divisors.