The analysis of nonlinear Kronig-Penney superlattice by a two-dimensional real-valued map

Abstract

The wave transportation in nonlinear Kronig-Penney model is investigated by a two-dimensional real map.The maps for different nonlinear parameters under the condition of fixed wave vector are calculated, and the corresponding evolution of the square of wave displacement along the nonlinear superlattice is also numerically calculated. The nonlinear parameter of the nonlinear Kronig-Penny superlattice has a distinctive modulation effect on the Bloch wave vector of the wave function in the superlattice. In response to the increase of the nonlinear parameter, the map evolutes from a finite number of dots to a closed orbit or an attractor, which corresponds to a periodic function, quasiperiodic function or chaos.