We consider the propagation of a shallow-water undular bore over a gentle monotonic
bottom slope connecting two regions of constant depth, in the framework of the variablecoefficient
Korteweg – de Vries equation. We show that, when the undular bore advances
in the direction of decreasing depth, its interaction with the slowly varying topography
results, apart from an adiabatic deformation of the bore itself, in the generation of a
sequence of isolated solitons — an expanding large-amplitude modulated solitary wavetrain
propagating ahead of the bore. Using nonlinear modulation theory we construct an
asymptotic solution describing the formation and evolution of this solitary wavetrain. Our
analytical solution is supported by direct numerical simulations. The presented analysis
can be extended to other systems describing the propagation of undular bores (dispersive
shock waves) in weakly non-uniform environments
