Infinite-Parameter ADHM Transform (2020)
Journal Article
Ward, R. (2021). Infinite-Parameter ADHM Transform. The Quarterly Journal of Mathematics, 72(1-2), 407-415. https://doi.org/10.1093/qmath/haaa054

The Atiyah–Drinfeld–Hitchin–Manin transform and its various generalizations are examples of nonlinear integral transforms between finite-dimensional moduli spaces. This note describes a natural infinite-dimensional generalization, where the transform... Read More about Infinite-Parameter ADHM Transform.

Hopf solitons on compact manifolds (2018)
Journal Article
Ward, R. (2018). Hopf solitons on compact manifolds. Journal of Mathematical Physics, 59(2), Article 022904. https://doi.org/10.1063/1.5006891

Hopf solitons in the Skyrme-Faddeev system on R3 typically have a complicated structure, in particular when the Hopf number Q is large. By contrast, if we work on a compact 3-manifold M, and the energy functional consists only of the Skyrme term (the... Read More about Hopf solitons on compact manifolds.

Integrable (2k)-Dimensional Hitchin Equations (2016)
Journal Article
Ward, R. (2016). Integrable (2k)-Dimensional Hitchin Equations. Letters in Mathematical Physics, 106(7), 951-958. https://doi.org/10.1007/s11005-016-0849-3

This letter describes a completely integrable system of Yang–Mills–Higgs equations which generalizes the Hitchin equations on a Riemann surface to arbitrary k-dimensional complex manifolds. The system arises as a dimensional reduction of a set of int... Read More about Integrable (2k)-Dimensional Hitchin Equations.

Symmetric Instantons and Discrete Hitchin Equations (2016)
Journal Article
Ward, R. (2016). Symmetric Instantons and Discrete Hitchin Equations. Journal of Integrable Systems, 1(1), Article xyw001. https://doi.org/10.1093/integr/xyw001

Self-dual Yang–Mills instantons on correspond to algebraic ADHM data. The ADHM equations for [Math Processing Error]-symmetric instantons give a one-dimensional integrable lattice system, which may be viewed as an discretization of the Nahm equations... Read More about Symmetric Instantons and Discrete Hitchin Equations.

Geometry of Solutions of Hitchin Equations on R^2 (2016)
Journal Article
Ward, R. (2016). Geometry of Solutions of Hitchin Equations on R^2. Nonlinearity, 29(3), Article 756. https://doi.org/10.1088/0951-7715/29/3/756

We study smooth SU(2) solutions of the Hitchin equations on ${{\mathbb{R}}^{2}}$ , with the determinant of the complex Higgs field being a polynomial of degree n. When $n\geqslant 3$ , there are moduli spaces of solutions, in the sense that the natur... Read More about Geometry of Solutions of Hitchin Equations on R^2.

Dynamics of monopole walls (2014)
Journal Article
Maldonado, R., & Ward, R. (2014). Dynamics of monopole walls. Physics Letters B, 734, 328-332. https://doi.org/10.1016/j.physletb.2014.05.072

The moduli space of centred Bogomolny–Prasad–Sommerfield 2-monopole fields is a 4-dimensional manifold M with a natural metric, and the geodesics on M correspond to slow-motion monopole dynamics. The best-known case is that of monopoles on R3, where... Read More about Dynamics of monopole walls.

Geometry of Periodic Monopoles (2013)
Journal Article
Maldonado, R., & Ward, R. (2013). Geometry of Periodic Monopoles. Physical Review D, 88(12), Article 125013. https://doi.org/10.1103/physrevd.88.125013

Bogomol’nyi-Prasad-Sommerfield monopoles on R 2 ×S 1 correspond, via the generalized Nahm transform, to certain solutions of the Hitchin equations on the cylinder R×S 1 . The moduli space M of two monopoles with their center of mass fixed is a four-d... Read More about Geometry of Periodic Monopoles.

Moduli of monopole walls and amoebas. (2012)
Journal Article
Cherkis, S., & Ward, R. (2012). Moduli of monopole walls and amoebas. Journal of High Energy Physics, 2012(5), Article 90. https://doi.org/10.1007/jhep05%282012%29090

We study doubly-periodic monopoles, also called monopole walls, determining their spectral data and computing the dimensions of their moduli spaces. Using spectral data we identify the moduli, and compare our results with a perturbative analysis. We... Read More about Moduli of monopole walls and amoebas..

Skyrmions and monopoles — isolated and arrayed (2011)
Journal Article
Ward, R. (2011). Skyrmions and monopoles — isolated and arrayed. Journal of Physics: Conference Series, 284(1), https://doi.org/10.1088/1742-6596/284/1/012005

There are two basic types of three-dimensional topological soliton, namely skyrmions and monopoles. This article reviews some of the features of such solitons, concentrating on static multi-skyrmions and multi-monopoles with structure group SU(2), an... Read More about Skyrmions and monopoles — isolated and arrayed.

Generalized Skyrme crystals (2010)
Journal Article
Silva Lobo, J., & Ward, R. (2011). Generalized Skyrme crystals. Physics Letters B, 696(3), 283-287. https://doi.org/10.1016/j.physletb.2010.12.037

This Letter deals with triply-periodic (crystalline) solutions in a family of Skyrme systems, namely where the field takes values in the squashed 3-sphere. The family includes the standard Skyrme model (round 3-sphere), and the Skyrme–Faddeev case (m... Read More about Generalized Skyrme crystals.

Skyrmion multi-walls. (2009)
Journal Article
Silva Lobo, J., & Ward, R. (2009). Skyrmion multi-walls. Journal of Physics A: Mathematical and Theoretical, 42(48), Article 482001. https://doi.org/10.1088/1751-8113/42/48/482001

Dynamics of periodic monopoles. (2009)
Journal Article
Harland, D., & Ward, R. (2009). Dynamics of periodic monopoles. Physics Letters B, 675(2), 262-266. https://doi.org/10.1016/j.physletb.2009.03.074

BPS monopoles which are periodic in one of the spatial directions correspond, via a generalized Nahm transform, to solutions of the Hitchin equations on a cylinder. A one-parameter family of solutions of these equations, representing a geodesic in th... Read More about Dynamics of periodic monopoles..

Chains of skyrmions. (2008)
Journal Article
Harland, D., & Ward, R. (2008). Chains of skyrmions. Journal of High Energy Physics, 2008(12), Article 093. https://doi.org/10.1088/1126-6708/2008/12/093

Walls and chains of planar skyrmions. (2008)
Journal Article
Harland, D., & Ward, R. (2008). Walls and chains of planar skyrmions. Physical Review D, 77(4), Article 045009. https://doi.org/10.1103/physrevd.77.045009

Monopole wall (2007)
Journal Article
Ward, R. (2007). Monopole wall. Physical Review D, Particles and fields, 75(2), Article 021701(R). https://doi.org/10.1103/physrevd.75.021701

We construct, numerically, a solution of the SU(2) Bogomolny equations corresponding to a sheet of BPS monopoles. It represents a domain wall between a vacuum region and a region of constant energy density, and it is the smoothed-out version of the p... Read More about Monopole wall.

Hopf solitons on the lattice. (2006)
Journal Article
Ward, R. (2006). Hopf solitons on the lattice. Journal of Physics A: Mathematical and Theoretical, 39(4), L105-L109. https://doi.org/10.1088/0305-4470/39/4/l05

Periodic monopoles (2005)
Journal Article
Ward, R. (2005). Periodic monopoles. Physics Letters B, 619(1-2), 177-183. https://doi.org/10.1016/j.physletb.2005.05.070

This Letter deals with static BPS monopoles in three dimensions which are periodic either in one direction (monopole chains) or two directions (monopole sheets). The Nahm construction of the simplest monopole chain is implemented numerically, and the... Read More about Periodic monopoles.

Planar Skyrmions: vibrational modes and dynamics (2005)
Journal Article
Piette, B., & Ward, R. (2005). Planar Skyrmions: vibrational modes and dynamics. Physica D: Nonlinear Phenomena, 201(1-2), 45-55. https://doi.org/10.1016/j.physd.2004.12.001

We study Skyrmion dynamics in a (2+1)-dimensional Skyrme model. The system contains a dimensionless parameter α, with α=0 corresponding to the O(3) sigma-model. If two Skyrmions collide head-on, then they can either coalesce or scatter—this depends o... Read More about Planar Skyrmions: vibrational modes and dynamics.

Skyrmions and Faddeev-Hopf solitons. (2004)
Journal Article
Ward, R. (2004). Skyrmions and Faddeev-Hopf solitons. Physical Review D, Particles and fields, 70(6),

Planar Skyrmions at high and low density. (2004)
Journal Article
Ward, R. (2004). Planar Skyrmions at high and low density. Nonlinearity, 17(3), 1033-1040. https://doi.org/10.1088/0951-7715/17/3/014

The O(3) Skyrme system in two space dimensions admits topological soliton solutions. This paper studies the transition between the high-density crystalline phase of such solitons and the low-density phase where there are multi-Skyrmions localized in... Read More about Planar Skyrmions at high and low density..