Multikink scattering in the ${\varphi }^6$ model revisited

Abstract

Antikink-kink ( $\bar{\mathrm{K}}$$\mathrm{K}$) collisions in the ${\varphi }^6$ model exhibit resonant scattering although the ${\varphi }^6$ kinks do not support any bound states to which energy could be transferred. In Phys. Rev. Lett. 107 (2011) 091602 it was conjectured that, instead, energy is transferred to a collective bound mode of the full $\bar{\mathrm{K}}$$\mathrm{K}$ configuration. Here we present further strong evidence for this conjecture. Further, we construct a collective coordinate model (CCM) for $\bar{\mathrm{K}}$$\mathrm{K}$ scattering based on this collective bound mode trapped between the $\bar{\mathrm{K}}$$\mathrm{K}$ pair which allows us to reproduce the full dynamics of $\bar{\mathrm{K}}$$\mathrm{K}$ scattering with striking accuracy. We also study kink-antikink ($\mathrm{K}$$\bar{\mathrm{K}}$) scattering and its description by a CCM. In this case a significant role of radiation is discovered.

17 pages, 17 figures

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