Parametrically Driven Nonlinear Oscillators with an Impurity

By virtue of the method of multiple scales, we study a chain of
parametrically driven nonlinear oscillators with a mass impurity. An equation is presented to describe the nonlinear wave of small amplitude in the chain. In our derivation, the equation is applicable to any eigen mode of coupled pendulum. Our result shows that a nonpropagation soliton emerges as the lowest or highest eigen mode of coupled pendulum is excited, and the impurity tends to pin the nonpropagation soliton excitation.