  In this paper, we present a novel class of high-order energy-preserving
schemes for solving the Zakharov-Rubenchik equations. The main idea of the
scheme is first to introduce an quadratic auxiliary variable to transform the
Hamiltonian energy into a modified quadratic energy and the original system is
then reformulated into an equivalent system which satisfies the mass, modified
energy as well as two linear invariants. The symplectic Runge-Kutta method in
time, together with the Fourier pseudo-spectral method in space is employed to
compute the solution of the reformulated system. The main benefit of the
proposed schemes is that it can achieve arbitrarily high-order accurate in time
and conserve the three invariants: mass, Hamiltonian energy and two linear
invariants. In addition, an efficient fixed-point iteration is proposed to
solve the resulting nonlinear equations of the proposed schemes. Several
experiments are addressed to validate the theoretical results.
