Purpose. In this paper, we investigate collective dynamic effects in a non-integrable φ4 model with three identical point-like attractive impurities. We study the excitation process and subsequent evolution of longlived localized oscillations (impurity modes) initiated by the passage of a kink through the impurity system.

Methods. The study is conducted using a combined approach that integrates analytical methods with direct numerical simulation. Within the analytical framework, based on the method of collective variables for small oscillation amplitudes, a system of coupled linear differential equations is derived to describe the dynamics of three oscillators.

Results. The solution of this system allowed for the determination of the collective excitation spectrum, consisting of three distinct normal mode frequencies. The dependence of these frequencies on the distance between the impurities is analyzed, demonstrating their splitting at small distances and asymptotic convergence to the single-impurity frequency as the distance increases. Numerical solution of the original nonlinear partial differential equation confirmed the existence of three modes and allowed for a detailed study of their dynamics. It has been established that, depending on the initial kink velocity and the distance between the impurities, various types of oscillations can be excited: the first mode (in-phase oscillations), the second mode (oscillations of the outer waves in anti-phase with a stationary central one), and the third mode, characterized by the anti-phase motion of the central impurity relative to the outer ones. It was found that the second and third modes exhibit a thresholdlike localization: they contribute to the dynamics only upon reaching a critical distance, when their frequency drops below √2. A comparison of analytical and numerical results showed good quantitative agreement for large distances and a systematic discrepancy for small ones, attributed to the nonlinearity of the potential.

Conclusion. The results of the work demonstrate that the introduction of a third impurity leads to a qualitative increase in the complexity of the system dynamics, which opens up possibilities for controlling nonlinear waves in media with multiple impurities.