Scattering between wobbling kinks

TL;DR

This study numerically investigates how wobbling kinks and antikinks in the $^4$ model scatter, revealing complex resonance structures and dependencies on initial conditions.

Contribution

It provides new insights into the scattering dynamics of wobbling kinks, including the influence of initial wobbling amplitude and velocity on final states.

Findings

Fractal resonance structures emerge with new windows.

Final wobbling amplitude depends linearly on collision velocity.

Final wobbling frequency decreases with collision velocity.

Abstract

In this paper the scattering between a wobbling kink and a wobbling antikink in the standard $\phi^4$ model is numerically investigated. The dependence of the final velocities, wobbling amplitudes and frequencies of the scattered kinks on the collision velocity and on the initial wobbling amplitude is discussed. The fractal structure becomes more intricate due to the emergence of new resonance windows and the splitting of those arising in the non-excited kink scattering. Outside this phase the final wobbling amplitude exhibits a linear dependence of the collision velocity whereas the final frequency is a decreasing function. By contrast these magnitudes are almost independent of the initial wobbling amplitude.