  A simple mechanical analog describing Landau-Zener tunneling effect is
proposed using two weakly coupled chains of nonlinear oscillators with
gradually decreasing (first chain) and increasing (second chain) masses. The
model allows to investigate nonlinear generalization of Landau-Zener tunneling
effect considering soliton propagation and tunneling between the chains. It is
shown that soliton tunneling characteristics become drastically dependent on
its amplitude in nonlinear regime. The validity of the developed tunneling
theory is justified via comparison with direct numerical simulations on
oscillator ladder system.
