Backward- and forward-wave soliton coexistence due to second-neighbor coupling in a left-handed transmission line

We study analytically and numerically the impact of second-neighbor interactions on propagation an initial wave-packet through a coupled nonlinear left-handed transmission line. start with detailed analysis dispersion curve group velocity. then use quasi-discrete approximation respect to long wavelength transverse perturbations reduce discrete model lattice Schrödinger equation. A product velocity (P) term (Q) is presented relevant parameters system. Here we see important role coupling, which makes non-monotonic. Thus, for given frequency, can be both positive negative, while each choice product, PQ, either or negative. Our numerical results confirm that sufficiently strong bright backward-wave pulses dark solitons coexist at common these travel in opposite directions lattice.