  We theoretically studied the interface states of liquid surface waves
propagating through the heterojunctions formed by a bottom with one-dimensional
periodic undulations. Via considering the periodic structure as a homogeneous
one, our systematic study shows that the signs of the effective depth and
gravitational acceleration are opposite within the band gaps no matter the
structure is symmetric or asymmetric. Those effective parameters can be used to
predict the interface states which could amplify the amplitudes of liquid
surface waves. These phenomena provide new opportunities to control the
localization of water-wave energy.
