  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 $\phi^4$ 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.
