A new hierarchy of integrable system of 1+2 dimensions: from Newton's law to generalized Hamiltonian system. Part II

The Hamiltonian equation provides us an alternate description of the basic physical laws of motion, which is used to be described by Newton’s law. The research on Hamiltonian integrable systems is one of the most important topics in the theory of solitons. This article proposes a new hierarchy of integrable systems of 1 + 2 dimensions with its Hamiltonian form by following the residue approach of Fokas and Tu. The new hierarchy of integrable system is of fundamental interest in studying the Hamiltonian systems.