Alternative SU(N) Skyrme models and their solutionsHarmonic maps from S 2 to CP NϪ1 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 Bϭ3Ϫ6 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.

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 ones͒ is /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.

We investigate properties of self-gravitating isorotating Skyrmions in the generalized Einstein-Skyrme model with higher-derivative terms in the matter field sector. These stationary solutions are axially symmetric, regular and asymptotically flat. We provide a detailed account of the branch structure of the spinning solutions in the topological sector of degree one. We show that additional branches of solutions appear, as the angular frequency increases above some critical value, these "cloudy" configurations can be considered as a bound system of the spinning Skyrmions and "pion" excitations in the topologically trivial sector. Considering the critical behavior of the isorotating solitons in the general Einstein-Skyrme model, we point out that there is no isospinning regular solutions in the reduced self-dual L 6 + L 0 submodel for any non zero value of the angular frequency.

Recently we have presented in [1] an ansatz which allows us to construct skyrmion fields from the harmonic maps of S 2 to CP N −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.

Abstract. This paper deals with classical solutions of the modified chiral model on R 2+1 . Such solutions are shown to correspond to products of various factor 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.

No abstract

This paper deals with various interrelations between strings and surfaces in three dimensional ambient space, two dimensional integrable models and two dimensional and four dimensional decomposed SU(2) Yang-Mills theories. Initially, a spinor version of the Frenet equation is introduced in order to describe the differential geometry of static three dimensional string-like structures. Then its relation to the structure of the su(2) Lie algebra valued Maurer-Cartan one-form is presented; while by introducing time evolution of the string a Lax pair is obtained, as an integrability condition. In addition, it is show how the Lax pair of the integrable nonlinear Schrödinger equation becomes embedded into the Lax pair of the time extended spinor Frenet equation and it is described how a spinor based projection operator formalism can be used to construct the conserved quantities, in the case of the nonlinear Schrödinger equation. Then the Lax pair structure of the time extended spinor Frenet equation is related to properties of flat connections in a two dimensional decomposed SU(2) Yang-Mills theory. In addition, the connection between the decomposed Yang-Mills and the Gauß-Godazzi equation that describes surfaces in three dimensional ambient space is presented. In that context the relation between isothermic surfaces and integrable models is discussed. Finally, the utility of the Cartan approach to differential geometry is considered. In particular, the similarities between the Cartan formalism and the structure of both two dimensional and four dimensional decomposed SU(2) Yang-Mills theories are discussed, while the description of two dimensional integrable models as embedded structures in the four dimensional decomposed SU(2) Yang-Mills theory are presented.

No abstract