Scattering of kinks of the sinh-deformed φ4\varphi^4 model

We consider the scattering of kinks of the sinh-deformed $\varphi^4$ model, which is obtained from the well-known $\varphi^4$ model by means of the deformation procedure. Depending on the initial velocity $v_{in}$ of the colliding kinks, different collision scenarios are realized. There is a critical value $v_{cr}$ of the initial velocity, which separates the regime of reflection (at $v_{in}>v_{cr}$) and that of a complicated interaction (at $v_{in}<v_{cr}$) with kinks' capture and escape windows. Besides that, at $v_{in}$ below $v_{cr}$ we observe the formation of a bound state of two oscillons, as well as their escape at some values of $v_{in}$.Comment: 23 pages, 12 figures; v2: minor changes to match version published in EPJ

Kink excitation spectra in the (1+1)-dimensional φ8\varphi^8 model

We study excitation spectra of BPS-saturated topological solutions -- the kinks -- of the $\varphi^8$ scalar field model in $(1+1)$ dimensions, for three different choices of the model parameters. We demonstrate that some of these kinks have a vibrational mode, apart from the trivial zero (translational) excitation. One of the considered kinks is shown to have three vibrational modes. We perform a numerical calculation of the kink-kink scattering in one of the considered variants of the $\varphi^8$ model, and find the critical collision velocity v_{\scriptsize \mbox{cr}} that separates the different collision regimes: inelastic bounce of the kinks at v_{\scriptsize \mbox{in}}\ge v_{\scriptsize \mbox{cr}}, and capture at v_{\scriptsize \mbox{in}}. We also observe escape windows at some values of v_{\scriptsize \mbox{in}} where the kinks escape to infinity after bouncing off each other two or more times. We analyse the features of these windows and discuss their relation to the resonant energy exchange between the translational and the vibrational excitations of the colliding kinks.Comment: 20 pages, 14 figures; V2: minor changes to match version published in JHE