  We propose a meshless conservative Galerkin method for solving Hamiltonian
wave equations. We first discretize the equation in space using radial basis
functions in a Galerkin-type formulation. Differ from the traditional RBF
Galerkin method that directly uses nonlinear functions in its weak form, our
method employs appropriate projection operators in the construction of the
Galerkin equation, which will be shown to conserve global energies. Moreover,
we provide a complete error analysis to the proposed discretization. We further
derive the fully discretized solution by a second order average vector field
scheme. We prove that the fully discretized solution preserved the discretized
energy exactly. Finally, we provide some numerical examples to demonstrate the
accuracy and the energy conservation.
