Theodora Ioannidou

Soliton solutions and nontrivial scattering in an integrable chiral model in (2+1) dimensions

The behavior of solitons in integrable theories is strongly constrained by the integrability of the theory; i.e., by the existence of an infinite number of conserved quantities that these theories are known to possess. One usually expects the scattering of solitons in such theories to be rather simple, i.e., trivial. By contrast, in this paper we generate new soliton solutions for the planar integrable chiral model whose scattering properties are highly nontrivial; more precisely, in head‐on collisions of N indistinguishable solitons the scattering angle (of the emerging structures relative to the incoming ones) is π/N. We also generate soliton–antisoliton solutions with elastic scattering; in particular, a head‐on collision of a soliton and an antisoliton resulting in 90° scattering.

Solutions of the modified chiral model in (2+1) dimensions

In this paper we deal with classical solutions of the modified chiral model on R2+1. Such solutions are shown to correspond to products of various factors which we call time-dependent unitons. Then the problem of solving the system of second-order partial differential equations for the chiral field is reduced to solving a sequence of systems of first-order partial differential equations for the unitons.

Spherically symmetric solutions of the SU(N) Skyrme models

Recently we have presented an ansatz which allows us to construct skyrmion fields from the harmonic maps of S2 to CPN−1. In this paper we examine this construction in detail and use it to construct, in an explicit form, new static spherically symmetric solutions of the SU(N) Skyrme models. We also discuss some properties of these solutions.

SU(N) skyrmions and harmonic maps

Harmonic maps from S2 to CPN−1 are introduced to construct low-energy configurations of the SU(N) Skyrme model. We show that one of such maps gives an exact, topologically trivial, solution of the SU(3) model. We study various properties of these maps and show that, in general, their energies are only a little higher than the energies of the corresponding SU(2) embeddings. Moreover, we show that the baryon and energy densities of the SU(3) configurations with baryon number B=3−6 are more symmetrical than their SU(2) analogs, thus suggesting that there exist solutions of the model with these symmetries. We also show that any SU(2) solution embedded into the SU(4) Skyrme model becomes a topologically trivial solution of this model.

Spinning gravitating skyrmions

We investigate self-gravitating rotating solutions in the Einstein-Skyrme theory. These solutions are globally regular and asymptotically flat. We present a new kind of solutions with zero baryon number, which possess neither a flat limit nor a static limit.

Kink dynamics in a lattice model with long-range interactions

This paper proposes a one-dimensional lattice model with long-range interactions which, in the continuum, keeps its nonlocal behaviour. In fact, the long-time evolution of the localized waves is governed by an asymptotic equation of the Benjamin-Ono type and allows the explicit construction of moving kinks on the lattice. The long-range particle interaction coefficients on the lattice are determined by the Benjamin-Ono equation.

Monopoles and harmonic maps

Recently Jarvis has proved a correspondence between SU(N) monopoles and rational maps of the Riemann sphere into flag manifolds. Furthermore, he has outlined a construction to obtain the monopole fields from the rational map. In this paper we examine this construction in some detail and provide explicit examples for spherically symmetric SU(N) monopoles with various symmetry breakings. In particular we show how to obtain these monopoles from harmonic maps into complex projective spaces. The approach extends in a natural way to monopoles in hyperbolic space and we use it to construct new spherically symmetric SU(N) hyperbolic monopoles.

Spontaneous symmetry breaking in wormholes spacetimes with matter

When bosonic matter in the form of a complex scalar field is added to Ellis wormholes, the phenomenon of spontaneous symmetry breaking is observed. Symmetric solutions possess full reflection symmetry with respect to the radial coordinate of the two asymptotically flat spacetime regions connected by the wormhole, whereas asymmetric solutions do not possess this symmetry. Depending on the size of the throat, at bifurcation points pairs of asymmetric solutions arise from or merge with the symmetric solutions. These asymmetric solutions are energetically favoured. When the backreaction of the boson field is taken into account, this phenomenon is retained. Moreover, in a certain region of the solution space both symmetric and asymmetric solutions exhibit a transition from single throat to double throat configurations.

The energy of scattering solitons in the Ward model

The energy density of a scattering soliton solution in Wards integrable chiral model is shown to be instantaneously the same as the energy density of a static multi-lump solution of the sigma model. This explains the quantization of the total energy in the Ward model.

Soliton dynamics in 3D ferromagnets

Abstract We study the dynamics of solitons in a Landau–Lifshitz equation describing the magnetization of a three-dimensional ferromagnet with an easy axis anisotropy. We numerically compute the energy dispersion relation and the structure of moving solitons, using a constrained minimization algorithm. We compare the results with those obtained using an approximate form for the moving soliton, valid in the small momentum limit. We also study the interaction and scattering of two solitons, through a numerical simulation of the (3+1)-dimensional equations of motion. We find that the force between two solitons can be either attractive or repulsive depending on their relative internal phase and that in a collision two solitons can form an unstable oscillating loop of magnons.