  We generalize the energy-based discontinuous Galerkin method proposed in
[SIAM J. Num. Anal., 53(6):2705-2726, 2015.] to second-order semilinear wave
equations. A stability and convergence analysis is presented along with
numerical experiments demonstrating optimal convergence for certain choices of
the interelement fluxes. Applications to the sine-Gordon equation include
simulations of breathers, kink, and anti-kink solitons.
