Scattering between orthogonally wobbling kinks

Abstract

The resonant energy transfer mechanism, responsible for the presence of fractal patterns in the velocity diagrams of kink-antikink scattering, is analyzed for a family of two-component scalar field theory models, in which the kink solutions have two shape modes (one longitudinal and one orthogonal to the kink orbit), in addition to the zero mode, and in which energy redistribution can occur among these three discrete modes. We investigate the scattering between wobbling kinks whose orthogonal shape mode is initially excited, examining how the final velocities, amplitudes, and frequencies depend on the initial excitation amplitude. The differences that this model presents with respect to the ${\varphi }^4$ model and its novel properties are highlighted. This analysis sheds light on the intricate dynamics that arise from the interplay between multiple degrees of freedom in kink scattering processes, offering insights distinct from those observed in simpler models.