On the propagation of nonlinear signals in nonlinear transmission lines

A quintic nonlinear Schrödinger (NLS) equation, with derivative cubic terms, that governs the propagation of nonlinear signals in a nonlinear transmission line (NLTL) is considered. By combining a special phase-imprint transformation with a modified lens transformation, we reduce the equation under consideration to a standard cubic NLS equation with a time-varying gain/loss term and obtain the integrability condition. Under this condition, we first apply a superposition procedure to derive new nonlinear wave signals that propagate with periodic amplitude in the NLTL. Secondly, in the absence of any gain/loss term in the cubic NLS equation, we apply the Darboux transformation to the derived new bright solitonlike signal of the NLTL. For a special form of the gain/loss term of the cubic NLS equation, we combine the homogeneous balance principle and an F-expansion technique to show the propagation of both bright and dark soliton-like signals in the NLTL under consideration, and show how to manage the soliton motion in the line.