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We prove the existence and uniqueness of a static and radially symmetric BPS monopole of unit topological charge in an arbitrary (4p – 1)-dimensional space descended from the generalized Yang–Mills theory in 4p dimensions and formulated and presented in a recent study of Radu and Tchrakian. This monopole solution also gives rise to an electrically and magnetically charged soliton, called dyon, in the same spacetime setting through the well-known Julia–Zee correspondence. Our method is based on a dynamical shooting approach depending on two shooting parameters which provides an effective framework for constructing the BPS monopole and dyon solutions in general dimensions.

We prove the existence of multisolitons in the gauged self-dual Maxwell and Chern–Simons sigma models with broken symmetry. In the context of topological solutions, the existence proofs rely on established results on earlier models. In the context of nontopological solutions with radial symmetry, the proof is by adapting a shooting argument.

We establish the existence and uniqueness of radially symmetric self-dual topological vortices in thep=2 members of the hierarchies of (generalised) Chern-Simons Higgs and Abelian Higgs models. We also obtain all possible symmetric nontopological vortices in the Chern-Simons model characterised by an additional parameter governing the decay rates of the fields.

String-like static solutions of the Einstein matter-gauge equations have interesting implications in cosmology. It has been shown recently that, at a critical coupling phase, this system of equations allows a reduction into a coupled Einstein-Bogomol'nyi system. In this Letter, we prove that, in the important case where the underlying two-dimensional Riemannian manifold is either compact or asymptotically Euclidean, the two systems are actually equivalent. Moreover, we show that the standard assumption that the strings reside in a conformally Euclidean surface will give us a metric which fails to be asymptotically Euclidean. In particular, in the radially symmetric case, we establish under the finite energy condition the boundary behavior of the metric. These results may indicate that a string solution will inevitably lead to nonflatness of the space at infinity even on the cross-section.

In the recently discovered Chern-Simons model, the reduction to a Bogomol'nyi bound or self-duality depends crucially on the specific form of the Higgs potential energy function, which is characterized by a φ6 type self-interaction. The purpose of this paper is to show that a much wider class of Higgs self-interaction may be allowed to achieve self-duality provided that the kinetic energy term of the Higgs scalar is suitably modified. The existence of topological multivortex solutions is also established. Furthermore, it is remarked that the Meissner effect may occur in the model.

The Bardeen-Cooper-Schrieffer integral equation with a positive kernel is studied in full generality. It is shown that, there exists a unique finite transition temperature, T c so that, if TT c ,the only solution of the equation is the trivial one, indicating the occurrence of the normal phase. Moreover, it is demonstrated that such a positive solution may be approximated by a sequence of solutions of the equation restricted on bounded domains. This latter result provides a useful computational scheme for the problem.

The existence of self-dual or anti-self-dual monopoles of a seven-dimensional generalized Yang-Mills-Higgs theory is proved using the second-order equations of motion. The behavior of solutions can be used to recognize self- or anti-self-duality. Moreover, it is shown that, in the class of the field configurations under discussion, the solutions are, in fact, unique.

The main result of this note is a proof of a conjecture of Burzlaff, O'Se and Tchrakian [1] concerning the existence of a certain kind of finite action solutions of the seven-dimensional generalized Yang-Mills-Higgs model derived from an eight-dimensional SO(8) Yang-Mills theory.

It is shown that the chiral angle, θ(r), of the hedgehog (symmetric) Skyrmions with an arbitrary baryon number, is a strictly decreasing or increasing function. For large values of r>0, θ(r) is strictly convex or concave. As r→∞, θ(r) and θ′(r) approach their limit values at the rate Or-αfor any α∈(0,2).