A NEW 2+1-DIMENSIONAL HAMILTONIAN INTEGRABLE SYSTEM

Abstract

It is shown that a new 2+1-dimensional second-order partial differential equation, when written as a first-order nonlinear evolutionary system, admits bi-Hamiltonian structure. Therefore, by Magri's theorem it is a completely integrable system. For this system a Lagrangian is introduced and Dirac's theory is applied in order to obtain first Hamiltonian structure. Then recursion operator is constructed and finally the second Hamiltonian structure for this system is obtained. Jacobi identity for the Hamiltonian structure is proved by using Olver's method. Thus, it is an example of a completely integrable system in three dimensions.