Kink dynamics in the MSTB Model

In this paper kink scattering processes are investigated in the Montonen-Sarker-Trullinger-Bishop model. The MSTB model is in fact a one-parametric family of relativistic scalar field theories living in a one-time one-space Minkowski space-time which encompasses two coupled scalar fields. Between the static solutions of the model two kinds of topological kinks are distinguished in a precise range of the family parameter. In that regime there exists one unstable kink exhibiting only one non-null component of the scalar field. Another type of topological kink solutions, stable in this case, includes two different kinks for which the two-components of the scalar field are non-null. Both one-component and two-component topological kinks are accompanied by their antikink partner. The decay of disintegration of the unstable kink to one of the stable pair plus radiation is numerically computed. The pair of stable two-component kinks living respectively on upper and lower half-ellipses in field space belong to identical topological sectors in configuration space and provides an ideal playground to address several scattering events involving one kink and either its own antikinks or either the antikink of the other stable kink of the pair. By means of a numerical computation procedure we shall find and describe interesting physical phenomena. Bion (kink-antikink oscillations) formation, kink reflection, kink-antikink annihilation, kink transmutation and resonances are examples of these type of events. The appearance of these special phenomena emerging in kink-antikink scattering configurations depends critically on the initial collision velocity and the chosen value of the coupling constant parametrizing the family of MSTB models.