This work is devoted to investigating weakly nonlinear hyperbolic waves arising from the action of small‐amplitude, high‐frequency boundary disturbances. By directly introducing a nonlinear phase variable corresponding to the leading wavefront and specifying a single‐wave‐mode boundary disturbance, we are able to construct an asymptotic solution. Furthermore, our result shows that, by properly arranging the relation of small amplitude to high frequency, a systematic procedure can be provided for constructing weakly nonlinear wave solutions with interior shocks and determining the shock initiation position (and time) when there is a local linear degeneracy at the leading wa
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