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

Transient traveling breather response of strongly anharmonic array of self-sustained oscillators: Analytical study

In the present study, we analyze the transient response of a locally excited chain of strongly anharmonic self-sustained oscillators. This discrete system under consideration models the dynamics of genuinely nonlinear, aeroelastic metamaterial. We particularly focus on the transient evolution of the traveling dissipative breathers, forming in locally excited, finite chains of self-sustained oscillators. The genuinely anharmonic nature of the system under consideration turns the asymptotic analysis of the transient regimes arising in this type of model into a highly challenging task. In the present study, we formulate a special analytical approach which allows for a simple, explicit, and fairly accurate analytical description of the amplitude evolution of the breather core towards the steady state as well as its instantaneous position.

Experimental study of intrinsic localized mode mobility in a cyclic, balanced, 1D nonlinear transmission line

Mobile intrinsic localized modes (ILMs) in balanced nonlinear capacitive-inductive cyclic transmission lines are studied by experiment, using a spatiotemporal driver under damped steady-state conditions. Without nonlinear balance, the experimentally observed resonance between the traveling ILM and normal modes of the nonlinear transmission line generates lattice drag via the production of a lattice backwave. In our experimental study of a balanced running ILM in a steady state, it is observed that the fundamental resonance can be removed over extended, well-defined driving frequency intervals and strongly suppressed over the complete ILM driving frequency range. Because both of these nonlinear capacitive and inductive elements display hysteresis our observation demonstrates that the experimental system, which is only partially self-dual, is surprisingly tolerant, regarding the precision necessary to eliminate the ILM backwave. It appears that simply balancing the cell dual nonlinearities makes the ILM envelope shape essentially the same at the two locations in the cell, so that the effective lattice discreteness seen by the ILM nearly vanishes.