Coupled backward- and forward-propagating solitons in a composite right/left-handed transmission line

We study the coupling between backward- and forward-propagating wave modes, with the same group velocity, in a composite right/left-handed nonlinear transmission line. Using an asymptotic multiscale expansion technique, we derive a system of two coupled nonlinear Schr{\"o}dinger equations governing the evolution of the envelopes of these modes. We show that this system supports a variety of backward- and forward propagating vector solitons, of the bright-bright, bright-dark and dark-bright type. Performing systematic numerical simulations in the framework of the original lattice that models the transmission line, we study the propagation properties of the derived vector soliton solutions. We show that all types of the predicted solitons exist, but differ on their robustness: only bright-bright solitons propagate undistorted for long times, while the other types are less robust, featuring shorter lifetimes. In all cases, our analytical predictions are in a very good agreement with the results of the simulations, at least up to times of the order of the solitons' lifetimes

Quasi-discrete microwave solitons in a split ring resonator-based left-handed coplanar waveguide

We study the propagation of quasi-discrete microwave solitons in a nonlinear left-handed coplanar waveguide coupled with split ring resonators. By considering the relevant transmission line analogue, we derive a nonlinear lattice model which is studied analytically by means of a quasi-discrete approximation. We derive a nonlinear Schr{\"o}dinger equation, and find that the system supports bright envelope soliton solutions in a relatively wide subinterval of the left-handed frequency band. We perform systematic numerical simulations, in the framework of the nonlinear lattice model, to study the propagation properties of the quasi-discrete microwave solitons. Our numerical findings are in good agreement with the analytical predictions, and suggest that the predicted structures are quite robust and may be observed in experiments

From Solitons to Rogue Waves in Nonlinear Left-Handed Metamaterials

In the present work, we explore soliton and rogue-like wave solutions in the transmission lineanalogue of a nonlinear left-handed metamaterial. The nonlinearity is expressed through a voltagedependentand symmetric capacitance motivated by the recently developed ferroelectric bariumstrontium titanate (BST) thin lm capacitor designs. We develop both the corresponding nonlineardynamical lattice, as well as its reduction via a multiple scales expansion to a nonlinear Schrodinger(NLS) model for the envelope of a given carrier wave. The reduced model can feature either afocusing or a defocusing nonlinearity depending on the frequency (wavenumber) of the carrier.We then consider the robustness of dierent types of solitary waves of the reduced model withinthe original nonlinear left-handed medium. We nd that both bright and dark solitons persist ina suitable parametric regime, where the reduction to the NLS is valid. Additionally, for suitableinitial conditions, we observe a rogue wave type of behavior, that diers signicantly from the classicPeregrine rogue wave evolution, including most notably the breakup of a single Peregrine-like patterninto solutions with multiple wave peaks. Finally, we touch upon the behavior of generalized membersof the family of the Peregrine solitons, namely Akhmediev breathers and Kuznetsov-Ma solitons,and explore how these evolve in the left-handed transmission line

On the Existence of Solutions Connecting IK Singularities and Impasse Points in Fully Nonlinear RLC Circuits

Higher-dimensional nonlinear and perturbed systems of implicit ordinary differential equations are studied by means of methods of dynamical systems. Namely, the persistence of solutions are studied under nonautonomous perturbations connecting either impasse points with IK-singularities or two impasse points. Important parts of the paper are applications of the theory to concrete perturbed fully nonlinear RLC circuit