  In this work we present a new class of real scalar field models admitting
strongly interactive kink solutions. Instead of the usual exponential
asymptotic behavior these topological solutions exhibit a power-law one. We
investigate the interaction force between a pair of kink/anti-kink solutions
both analytically and numerically, by integrating the time dependent field
equations of the model. Furthermore, working within the first-order framework,
we analyze the linear stability of these solutions. The stability analysis
leads to Sch\"odinger-like equations with potentials which, despite admitting
no bound states, lead to strong resonance peaks. We argue that these properties
are important for some possible physical applications.
