Related papers: High energy density in the collision of $N$ kinks …
Solitons are very effective in transporting energy over great distances and collisions between them can produce high energy density spots of relevance to phase transformations, energy localization and defect formation among others. It is…
In our recent study the maximal values of kinetic and potential energy densities that can be achieved in the collisions of $N$ slow kinks in the sine-Gordon model were calculated analytically (for $N=1,2$, and 3) and numerically (for $4\le…
We study simultaneous collisions of two, three, and four kinks and antikinks of the $\phi^6$ model at the same spatial point. Unlike the $\phi^4$ kinks, the $\phi^6$ kinks are asymmetric and this enriches the variety of the collision…
The maximal energy density that can be achieved in the collisions of the particle-like wave trains in the $\phi^4$ model has been investigated numerically for different wave train parameters. From these results the prediction is made on how…
We study collisions of two, three, and four kinks of the double sine-Gordon model. The initial conditions are taken in a special form in order to provide collision of all kinks in one point. We obtain dependences of the maximal energy…
We study collisions of kinks in the one-space and one-time dimensional noncanonical nonintegrable scalar $\phi^{6}$ model. We examine the energy density of the kink, and we find that, as a function of the parameters that control the…
We compute semiclassical corrections to the energy density of kinks in $\phi^4$ theory and of solitons in the sine-Gordon model in $1+1$ dimensions, using local and covariant renormalization techniques from quantum field theory in curved…
The transition from integrable to non-integrable highly-dispersive nonlinear models is investigated. The sine-Gordon and $\phi^4$-equations with the additional fourth-order spatial and spatio-temporal derivatives, describing the higher…
We revisit the problem of the three-soliton collisions in the weakly perturbed sine-Gordon equation and develop an effective three-particle model allowing to explain many interesting features observed in numerical simulations of the soliton…
Extending a recent effective theory formulation for the dynamics of kinks in the sine-Gordon model [1], we propose an analogous effective description of $\phi^4$ kinks. Three different reduced models based on the kink position, width and…
In the present study the interaction of a sine-Gordon kink with a localized inhomogeneity is considered. In the absence of dissipation, the inhomogeneity considered is found to impose a potential energy barrier. The motion of the kink for…
We consider an enlarged $(1+1)$-dimensional model with two real scalar fields, $\phi$ and $\chi$ whose scalar potential $V(\phi,\chi)$ has a standard $\chi^4$ sector and a sine-Gordon one for $\phi$. These fields are coupled through a…
The energy density is the prime parameter to define the deconfinement of quarks and gluons occurring in collisions of heavy ions. Recently, there is mounting evidence that many observables in proton-proton collisions behave in a manner very…
We analyze the non-equilibrium dynamics of the O(N) Phi^4 model in the large N limit and for states of large energy density. The dynamics is dramatically different when the energy density is above the top of the tree level potential V_0…
We review recent works on modeling of dynamics of kinks in 1+1 dimensional $\phi^4$ theory and other related models, like sine-Gordon model or $\phi^6$ theory. We discuss how the spectral structure of small perturbations can affect the…
We study the phenomenon of negative energy densities in quantum field theories with self-interaction. Specifically, we consider a class of integrable models (including the sinh-Gordon model) in which we investigate the expectation value of…
The nuclear symmetry energy as a function of density is rather poorly constrained theoretically and experimentally both below saturation density, but particularly at high density, where very few relevant experimental data exist. We discuss…
The two major effects observed in collisions of the continuum $\phi^4$ kinks are (i) the existence of critical collision velocity above which the kinks always emerge from the collision and (ii) the existence of the escape windows for…
We estimate the energy density pile-up at mid-rapidity in central Pb+Pb collisions from 2 - 200 GeV/nucleon. The energy density is decomposed into hadronic and partonic contributions. A detailed analysis of the collision dynamics in the…
In this report, the various 1D single soliton and multi-soliton solutions of the Sine-Gordon equation are explored. First the topological kink solitons and their properties for the Sine-Gordon, as well as the $\phi^{4}$ model are…