  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.
