  Localised structures appear in a wide variety of systems, arising from a
pinning mechanism due to the presence of a small-scale pattern or an imposed
grid. When there is a separation of lengthscales, the width of the pinning
region is exponentially small and beyond the reach of standard asymptotic
methods. We show how this behaviour can be obtained using a variational method,
for two systems. In the case of the quadratic-cubic Swift-Hohenberg equation,
this gives results that are in agreement with recent work using exponential
asymptotics. Secondly, the method is applied to a discrete system with
cubic-quintic nonlinearity, giving results that agree well with numerical
simulations.
