Autowaves in double-wire lines with the exponential-type nonlinear active element

The regimes corresponding to the appearance of localized excitation pulses in a nonlinear double-wire line with an exponential-type active element similar to that occurring in the distributed $p-n$ junctions and nerve fibers are studied on the basis of exact solutions. It is shown that the line of this type is described by the nonlinear telegraph equation if there is a running inductance and by the one-dimensional nonlinear diffusion equation if it is absent. The main properties of the excitation waves and conditions for their appearance are examined.