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 eigenmode of coupled pendulum. Our result shows that a nonpropagation soliton emerges as the lowest or highest eigenmode of coupled pendulum is excited, and the impurity tends to pin the nonpropagation soliton excitation.