Systems governed by non-linear differential equations are of fundamental
importance in all branches of science, but our understanding of them is
still extremely limited. In this book a particular system, describing
the interaction of magnetic monopoles, is investigated in detail. The
use of new geometrical methods produces a reasonably clear picture of
the dynamics for slowly moving monopoles. This picture clarifies the
important notion of solitons, which has attracted much attention in
recent years. The soliton idea bridges the gap between the concepts of
"fields" and "particles," and is here explored in a fully
three-dimensional context. While the background and motivation for the
work comes from physics, the presentation is mathematical.
This book is interdisciplinary and addresses concerns of theoretical
physicists interested in elementary particles or general relativity and
mathematicians working in analysis or geometry. The interaction between
geometry and physics through non-linear partial differential equations
is now at a very exciting stage, and the book is a contribution to this
activity.
Originally published in 1988.
The Princeton Legacy Library uses the latest print-on-demand
technology to again make available previously out-of-print books from
the distinguished backlist of Princeton University Press. These editions
preserve the original texts of these important books while presenting
them in durable paperback and hardcover editions. The goal of the
Princeton Legacy Library is to vastly increase access to the rich
scholarly heritage found in the thousands of books published by
Princeton University Press since its founding in 1905.
