Algebro-Geometric Solution to Two New (2+1)-Dimensional Modified Kadomtsev--Petviashvili Equations

Two new (2+1)-dimensional modified Kadomtsev--Petviashvili (mKP) equations are presented, which are related to a hierarchy of (1+1)-dimensional soliton equations. Through the nonlinearization of Lax pair and the Riemann--Jacobi inversion technique, the algebro-geometric solutions of both the mKP equations are obtained.