arXiv subjects
Publications and source records attributed to Theodora Ioannidou.
We present soliton and soliton-antisoliton solutions for the integrable chiral model in 2+1 dimensions with nontrivial (elastic) scattering. These solutions can be obtained either as the limiting cases of the ones already constructed by Ward or by adapting Uhlenbeck's method.
The O(3) sigma model in two spatial dimensions admits topological (Bogomol'nyi) lower bound on its energy. This paper proposes a lattice version of this system which maintains the Bogomol'nyi bound and allows the explicit construction of static solitons on the lattice. Numerical simulations show that these lattice solitons are unstable undersmall perturbations; in fact, their size changes linearly with time.
The behaviour 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 which 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 $90^0$ scattering.