Preface xi different areas of mathematics, soliton theory is generally only en- countered by specialists with advanced training. So, most of the books on the subject are written for researchers with doctorates in math or physics (and experience with both). And even the handful of books on soliton theory intended for an undergraduate audience tend to have expectations of prerequisites that will exclude many potential readers. However, it is precisely this interdisciplinary nature of soliton theory the way it brings together material that students would have learned in different math courses and its connections to science and engineering that make this subject an ideal topic for a single semester special topics class, “capstone” experience or reading course. This textbook was written with that purpose in mind. It assumes a minimum of mathematical prerequisites (essentially only a calculus sequence and a course in linear algebra) and aims to present that material at a level that would be accessible to any undergraduate math major. Correspondingly, it is not expected that this book alone will pre- pare the reader for actually working in this field of research as would many of the more advanced textbooks on this subject. Rather, the goal is only to provide a “glimpse” of some of the many facets of the mathematical gem that is soliton theory. Experts in the field are likely to note that many truly important topics have been ex- cluded. For example, symmetries of soliton equations, the Hamil- tonian formulation, applications to science and engineering, higher genus algebro-geometric solutions, infinite dimensional Grassmannian manifolds, and the method of inverse scattering are barely mentioned at all. Unfortunately, I could not see a way to include these topics without increasing the prerequisite assumptions and the length of the book to the point that it could no longer serve its intended purpose. Suggestions of additional reading are included in footnotes and at the end of most chapters for those readers who wish to go beyond the mere introduction to this subject that is provided here. On the Use of Technology This textbook assumes that the reader has access to the computer program Mathematica. For your convenience, an appendix to the book is provided which explains the basic use of this software and offers “troubleshooting” advice. In addition, at the time of this writ-
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