Outputs (4)

Two integrable systems related to hyperbolic monopoles. (1999)
Journal Article
Ward, R. (1999). Two integrable systems related to hyperbolic monopoles. Asian Journal of Mathematics, 3(1), 325-332. https://doi.org/10.4310/ajm.1999.v3.n1.a12

Monopoles on hyperbolic 3-space were introduced by Atiyah in 1984. This article describes two integrable systems which are closely related to hyperbolic monopoles: a one-dimensional lattice equation (the Braam-Austin or discrete Nahm equation), and a... Read More about Two integrable systems related to hyperbolic monopoles..

Hopf solitons on S3 and R3. (1999)
Journal Article
Ward, R. (1999). Hopf solitons on S3 and R3. Nonlinearity, 12(2), 241-246. https://doi.org/10.1088/0951-7715/12/2/005

The Skyrme–Faddeev system, a modified O(3) sigma model in three space dimensions, admits topological solitons with nonzero Hopf number. One may learn something about these solitons by considering the system on the 3-sphere of radius R. In particular,... Read More about Hopf solitons on S3 and R3..

Integrable systems: twistors, loop groups, and Riemann surfaces. (1999)
Book
Hitchin, N., Segal, G., & Ward, R. (1999). Integrable systems: twistors, loop groups, and Riemann surfaces. Oxford University Press

This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are int... Read More about Integrable systems: twistors, loop groups, and Riemann surfaces..

Lax pairs for integrable lattice systems (1999)
Journal Article
Ward, R. (1999). Lax pairs for integrable lattice systems. Journal of Mathematical Physics, 40(1), 299-308. https://doi.org/10.1063/1.532772

This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes the features... Read More about Lax pairs for integrable lattice systems.