Propagating intrinsic localized mode in a cyclic, dissipative, self-dual one-dimensional nonlinear transmission line

A well-known feature of a propagating localized excitation in a discrete lattice is the generation of a backwave in the extended normal mode spectrum. To quantify the parameter-dependent amplitude of such a backwave, the properties of a running intrinsic localized mode (ILM) in electric, cyclic, dissipative, nonlinear 1D transmission lines, containing balanced nonlinear capacitive and inductive terms, are studied via simulations. Both balanced and unbalanced damping and driving conditions are treated. The introduction of a unit cell duplex driver, with a voltage source driving the nonlinear capacitor and a synchronized current source, the nonlinear inductor, provides an opportunity to design a cyclic, dissipative self-dual nonlinear transmission line. When the self-dual conditions are satisfied, the dynamical voltage and current equations of motion within a cell become the same, the strength of the fundamental, resonant coupling between the ILM and the lattice modes collapses, and the associated fundamental backwave is no longer observed.

Automated summary

The properties of a running intrinsic localized mode (ILM) in electric, cyclic, dissipative, nonlinear 1D transmission lines are studied to quantify the parameter-dependent amplitude of the backwave. Balanced and unbalanced damping and driving conditions are considered. The design of a cyclic, dissipative self-dual nonlinear transmission line is achieved by introducing a unit cell duplex driver. When the self-dual conditions are satisfied, the fundamental backwave is no longer observed.