where and are, respectively, the current in and voltage across the lines, and and , both assumed strictly positive everywhere, are the inductance and capacitance per unit length. For the moment, we will leave aside the discussion of boundary conditions, and deal only with the Cauchy problem (i.e., we assume the spatial domain of the problem to be the entire axis). Note also that this system includes the vocal tract model (1.20) as a special case, under an appropriate set of variable and parameter replacements.

As discussed in §4.2.3, if we assume that and are constant, then the set of equations can be reduced to a single second order equation in the voltage alone^{}:

where the

This equation and its analogues in higher dimensions (see Appendix A) are collectively known as the