On the decomposition of the modified Kadometsev–Petviashvili equation and the connection between the KN equation and a completely integrable finite-dimensional Hamiltonian system

Abstract

The (2+1)-dimensional modified Kadomtsev–Petviashvili (mKP) equation is decomposed into the known (1+1)-dimensional Kaup–Newell (KN) equation. By using the nonlinearization of the Lax pair, a classically integrable Hamiltonian system in the Liouville sense and the involutive solution of the mKP equation (1.1) are obtained from the first two nontrivial KN equations.