  We consider propagating, spatially localised waves in a class of equations
that contain variational and non-variational terms. The dynamics of the waves
is analysed through a collective coordinate approach. Motivated by the
variational approximation, we show that there is a natural choice of projection
onto collective variables for reducing the governing (nonlinear) partial
differential equation (PDE) to coupled ordinary differential equations (ODEs).
This projection produces ODEs whose solutions are exactly the stationary states
of the effective Lagrangian that would be considered from applying the
variational approximation method. We illustrate our approach by applying it to
a modified Fisher equation for a travelling front, containing a
non-constant-coefficient nonlinear term. We present numerical results that show
that our proposed projection captures both the equilibria and the dynamics of
the PDE much more closely than previously proposed projections.
