Algebro-Geometric Solution to the Modified Kadomtsev–Petviashvili Equation

Abstract

The modified Kadomtsev–Petviashvili (mKP) equation is split into two soliton equations in the modified Jaulent–Miodek (mJM) hierarchy, and further into integrable finite-dimensional Hamiltonian systems (FDHSs) using the nonlinearization of Lax pairs. The Abel–Jacobi coordinate is introduced to linearize the mKP flow such that its solution is reduced as a linear superposition, expressed in the Abel–Jacobi variable. Finally, the algebro-geometric solution of the mKP equation is given via the Jacobi inversion.