Nonsimilarity solutions in closed-form, for a sufficiently energetic line-explosion, in the presence of a constant axial current, are obtained. The gaseous medium is of constant pressure and its density varies as some inverse power of the distance from the line of explosion; ω is the power index, lying in the interval 0⩽ω<2. The disturbance is headed by cylindrical shock surface of variable strength. The total energy of the wave is non-constant, but can be made to vary slowly with time.

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