Quasi-periodic solutions for some (2+1)-dimensional integrable models generated by the Jaulent-Miodek hierarchy

Some (2 + 1)-dimensional integrable models, including the modified Kadomtsev-Petviashvili equation, generated by the Jaulent-Miodek hierarchy are investigated. With the help of the Jaulent-Miodek eigenvalue problem, these (2 + 1)-dimensional integrable models are separated into compatible Hamiltonian systems of ordinary differential equations. Using the generating function flow method, the involutivity and the functional independence of the integrals are proved. The Abel-Jacobi coordinates are introduced, from which the quasi-periodic solutions for these (2 + 1)-dimensional integrable models are derived by resorting to the Riemann theta functions.