Evolution equations for long, nonlinear internal waves are derived when the basic stratified shear flow has a slow temporal and spatial variation as well as the usual dependence on the vertical coordinate. When the horizontal waveguide has a limited vertical extent the evolution equation is a variable coefficient Korteweg‐deVries equation, while in the deep fluid case the evolution equation is a variable coefficient Benjamin‐Davis‐Ono equation. Explicit expressions are obtained for the coefficients of these equa
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