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Recent studies have emphasized the important role that a shape deformabilityof scalar-field models pertaining to the same class with the standard $\phi^4$field, can play in controlling the production of a specific type of breathingbound states so-called oscillons. In the context of cosmology, the built-inmechanism of oscillons suggests that they can affect the standard picture ofscalar ultra-light dark matter. In the present work kink scatterings areinvestigated in a parametrized model of bistable system admitting the classical$\phi^4$ field as an asymptotic limit, with focus on the formation oflong-lived low-amplitude almost harmonic oscillations of the scalar fieldaround a vacuum. The parametrized model is characterized by a double-wellpotential with a shape-deformation parameter that changes only the steepness ofthe potential walls, and hence the flatness of the hump of the potentialbarrier, leaving unaffected the two degenerate minima and the barrier height.It is found that the variation of the deformability parameter promotes severaladditional vibrational modes in the kink-phonon scattering potential, leadingto suppression of the two-bounce windows in kink-antikink scatterings and theproduction of oscillons. Numerical results suggest that the anharmonicity ofthe potential barrier, characterized by a flat barrier hump, is the maindeterminant factor for the production of oscillons in double-well systems.

Kink-antikink scattering-induced breathing bound states and oscillons in a parametrized $\phi^4$ model