Department of Nonlinear Physics,
Saratov State University,
83 Astrakhanskaya Str.,
410012 Saratov,

Modeling of signal propagation in a nonlinear periodic structure

Simple models of nonlinear dispersive media, described by nonlinear Schroedinger equation and nonlinear Klein-Gordon equation were analyzed. The criterion that defines the character of modulational instability (of convective or of absolute type) in such systems was derived. Regimes of nonlinear tunneling were studied in details. It was shown that soliton tunneling takes place when modulational instability is absolute, and quasi-linear tunneling occurs when instability is convective. Developed theory was applied to interpret the results of numerical simulation of signal propagation in nonlinear periodic structure near cut-off frequency.