Abstract: Recently,Bridges et al.extended finite dimensional Hamiltonian system to infinite dimensional Hamiltonian system, based on the meaning of Hamiltonian mechanics.Introducing the new function coordinate,they made the partial differential equation having finite dimensional Hamiltonian symplectic structure in various directions of time and space.So the partial differential equation is determined by the finite symplectic structure and the gradient function of right side.The discrete algorithm of the conservation law of satisfying the multismplectic Hamiltonian system is called the multisymplectic algorithm.A numerical example is presented on the coupled nonlinear Schrödinger system treated the infinite dimensional Hamiltonian system.Numerical results cover the related transmission,reflection, and trapping after the colliding of the two solitions.

Key words: coupled nonlinear Schrödinger system, multisymplectic difference schemes