Collisions of kinks in deformed $\varphi^4$ and $\varphi^6$ models

Two hyperbolic-deformed field theoretic models are discussed. In both of them, due to the effect of specific deformation function on the well known $\varphi^4$ and $\varphi^6$ models, their internal structure may change significantly. Unlike the $\varphi^4$ kinks solutions, which has only one internal mode in addition to its translational mode, the kinks of the hyperbolic-deformed $\varphi^4$ model can have several internal modes. Moreover, the deformation on the $\varphi^6$ model has other interesting features, because the kinks of the $\varphi^6$ model have only a zero mode and the deformation may cause the appearance of internal mode for both kink and antikink. The presence of the new internal modes modify the collisions which we explore in the present work. The deformation relies on a real parameter, which controls the number of internal modes, and we also study how the deformation parameter alter the mass of the kinks and the critical velocities involved in the collisions.