Nonlinear Schrodinger equation, infinite-dimensional symplectic manifold or infinite-dimensional almost complex inner product manifold (Japanese)

While for a quadratic form in Hilbert space, we can consider a Schrodinger equation which has it as its Hamiltonian, here, we generalize this relationship and derive a nonlinear Schrodinger equation as the Hamiltonian system with a general function as its Hamiltonian. Furthermore, using this consideration as a stepping stone, we define an infinite-dimensional symplectic manifold and an infinite-dimensional Hamiltonian system on it.