Derivability of shock-scattering coefficients in the shock’s comoving frame

Determine whether the closed-form expressions for the small-amplitude “sound” wave reflection and transmission coefficients for scattering by a shock wave in a nonlinear transmission line can be derived by analyzing wave propagation in the reference frame moving with the shock wave, rather than by the jump-condition-based matching used to obtain those coefficients.

Background

The paper derives explicit formulas for the coefficients describing reflection and transmission of small-amplitude (linearized) waves when they interact with a shock wave in a nonlinear transmission line that can have both nonlinear capacitors and inductors. These coefficients are expressed in terms of relative wave speeds and effective impedances on either side of the shock and across the shock.

After presenting these results, the authors pose whether these same formulas could be obtained more directly from a transformation to the shock’s rest frame, i.e., by analyzing propagation in the frame of reference moving with the shock wave, rather than through the detailed matching via jump conditions. This raises the question of an alternative, potentially simpler derivation in the comoving frame.