Adiabatic motion of two-component BPS kinks

Abstract

The low energy dynamics of degenerated BPS domain walls arising in a generalized WessZumino model is described as geodesic motion in the space of these topological walls.

Changing shapes: adiabatic dynamics of composite solitary waves

“…The deformation of our choice comply with this requirement and, moreover, ensures integrability of the dynamical system to be solved in the search for kinks. Second, we shall show in Section §3 that the Hamilton characteristic function, the "superpotential" W I (φ) (16), is precisely the potential of the MSTB model. This fact links both systems in a hierarchal way.…”

“…For normal kinks, the dynamics is merely dictated by Lorentz invariance and thus characterized by shape invariance. We shall address the difficult issue of the evolution of composite solitary waves within the framework of Manton's adiabatic principle, see [22] and [16]: geodesics in the moduli space determine the slow motion of topological defects. In this scheme, the dynamics arises from the hypothesis that only the parameters of the moduli space a and b depend on time.…”

“…Apart from the center of the kink, there is a second integration constant; for large values of the second integration constant b solitary waves seem to be composed of two lumps of energy, whereas for b small they only show one lump. In References [15] and [16] we first unveiled the whole manifold of solitary waves of this model and then showed that in this system solitary waves can travel without dispersion, although changing the relative position of the two lumps.…”

Generalized MSTB models: Structure and kink varieties

“…The parameter γ 1 in (11) fixes the distance between the TK1 and TK2 kinks. In References [35,36] a description of the evolution of this distance in time has been worked out for slow speeds. Although we are dealing with non-linear systems, the adiabatic evolution of composite kinks can be dealt with as geodesic motion in the kink parameter space with respect to the metric induced by the field kinetic energy density, thus providing a good description of kink scattering at low energies.…”

Non-topological kink scattering in a two-component scalar field theory model

“…This fact allows the identification of all the static solitary wave solutions. The kink variety has also been analytically identified for the so called BNRT model, which was initially introduced by Bazeia, Nascimento, Ribeiro and Toledo [88,89] and studied later by other authors [90,91,92,93] in different contexts. In this case, the potential can be written as half the square of the gradient of a superpotential, which leads to first order equations using a Bogomolny arrangement of the energy functional.…”