  Furihata and Matsuo proposed in 2010 an energy-conserving scheme for the
Zakharov equations, as an application of the discrete variational derivative
method (DVDM).
  This scheme is distinguished from conventional methods (in particular the one
devised by Glassey in 1992) in that the invariants are consistent with respect
to time, but it has not been sufficiently studied both theoretically and
numerically.
  In this study, we theoretically prove the solvability under the loosest
possible assumptions.
  We also prove the convergence of this DVDM scheme by improving the argument
by Glassey.
  Furthermore, we perform intensive numerical experiments for comparing the
above two schemes.
  It is found that the DVDM scheme is superior in terms of accuracy, but since
it is fully-implicit, the linearly-implicit Glassey scheme is better for
practical efficiency.
  In addition, we proposed a way to choose a solution for the first step that
would allow Glassey's scheme to work more efficiently.
