Decomposition of certain nonlinear evolution equations and their quasi-periodic solutions

A new 2+1-dimensional nonlinear evolution equation is proposed. With the help of the known 1+1-dimensional soliton equations, this new 2+1-dimensional evolution equation and the modified Kadomtsev–Petviashvili equation 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 to straighten out the associated flows. The Riemann–Jacobi inversion problem is discussed, from which quasi-periodic solutions of the 1+1-dimensional soliton equations, the new 2+1-dimensional evolution equation and the modified Kadomtsev–Petviashvili equation are obtained.