Preface
By covering a carefully selected subset of topics, offering detailed
explanations and examples, and with the occasional assistance of
technology, this book aims to introduce undergraduate students to a
subject normally only encountered by graduate students and
researchers. Because of its interdisciplinary nature (bringing
together different branches of mathematics as well as having
connections to science and engineering), it is hoped that this book
would be ideal for a one semester special topics class, “capstone” or
reading course.
About Soliton Theory
There are many different phenomena in the real world which we de-
scribe as “waves”. For example, consider not only water waves but
also electromagnetic waves and sound waves. Because of tsunamis,
microwave ovens, lasers, musical instruments, acoustic considerations
in auditoriums, ship design, the collapse of bridges due to vibration,
solar energy, etc., this is clearly an important subject to study and
understand. Generally, studying waves involves deriving and solv-
ing some differential equations. Since these involve derivatives of
functions, they are a part of the branch of mathematics known to
professors as analysis and to students as calculus. But, in general,
the differential equations involved are so difficult to work with that
one needs advanced techniques to even get approximate information
about their solutions.
It was therefore a big surprise in the late 20th century when it
was realized for the first time that some of these equations are much
easier than they first appeared. These equations that are not as
difficult as people might have thought are called “soliton equations”
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