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In both the ocean and the atmosphere, the interaction of a density stratified flow with topography
can generate large-amplitude, horizontally propagating internal solitary waves. Often
these waves are observed in regions where the waveguide properties vary in the direction
of propagation. In this article we consider nonlinear evolution equations of the Kortewegde
Vries type, with variable coefficients, and use these models to review the properties of
slowly-varying periodic and solitary waves.