  We study the flow of water waves over bathymetry that varies periodically
along one direction. We derive a linearized, homogenized model and show that
the periodic bathymetry induces an effective dispersion, distinct from the
dispersion inherently present in water waves. We relate this dispersion to the
well-known effective dispersion introduced by changes in the bathymetry in
non-rectangular channels. Numerical simulations using the (non-dispersive)
shallow water equations reveal that a balance between this effective dispersion
and nonlinearity can create solitary waves. We derive a KdV-type equation that
approximates the behavior of these waves in the weakly-nonlinear regime. We
show that, depending on geometry, dispersion due to bathymetry can be much
stronger than traditional water wave dispersion and can prevent wave breaking
in strongly nonlinear regimes. Computational experiments using depth-averaged
water wave models %, as well as confirm the analysis and suggest that
experimental observation of these solitary waves is possible.
