  In this paper, a moving mesh discontinuous Galerkin (dG) method is developed
for nonlinear partial differential equations (PDEs) with traveling wave
solutions. The moving mesh strategy for one dimensional PDEs is based on the
rezoning approach which decouples the solution of the PDE from the moving mesh
equation. We show that the dG moving mesh method is able to resolve sharp wave
fronts and wave speeds accurately for the optimal, arc-length and curvature
monitor functions. Numerical results reveal the efficiency of the proposed
moving mesh dG method for solving Burgers', Burgers'-Fisher and
Schl\"ogl(Nagumo) equations.
