Wave-front solution in extended quantum circuits with charge discreteness

We study the capacitively coupled, quantum transmission line with charge discreteness, discussed in an earlier paper. Due to the difficulties of dealing with a highly nonlinear system, only a low-lying propagating wave solution was obtained then, the so-called cirquiton. In this work, we obtain a wave-front solution, valid for the long-wavelengh approximation. The propagation velocity v of the wave front depends on the (pseudo) flux parameter f; the physical requirement that v should be real implies the existence of allowed and forbidden regions (gaps) in the space of the parameter f. A study of the stability of the solutions is presented. We remark that it is possible to make a connection between our system and the (quantum) Toda lattice.