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We consider propagation of high-frequency wave packets along a smoothevolving background flow whose evolution is described by a simple-wave type ofsolutions of hydrodynamic equations. In geometrical optics approximation, themotion of the wave packet obeys the Hamilton equations with the dispersion lawplaying the role of the Hamiltonian. This Hamiltonian depends also on theamplitude of the background flow obeying the Hopf-like equation for the simplewave. The combined system of Hamilton and Hopf equations can be reduced to asingle ordinary differential equation whose solution determines the value ofthe background amplitude at the location of the wave packet. This approachextends the results obtained in Ref.~\cite{ceh-19} for the rarefactionbackground flow to arbitrary simple-wave type background flows. The theory isillustrated by its application to waves obeying the KdV equation.

Propagation of wave packets along intensive simple waves