  In this paper, one-stage explicit trigonometric integrators for solving
quasilinear wave equations are formulated and studied. For solving wave
equations, we first introduce trigonometric integrators as the
semidiscretization in time and then consider a spectral Galerkin method for the
discretization in space. We show that one-stage explicit trigonometric
integrators in time have second-order convergence and the result is also true
for the fullydiscrete scheme without requiring any CFL-type coupling of the
discretization parameters. The results are proved by using energy techniques,
which are widely applied in the numerical analysis of methods for partial
differential equations.
