6610
2d9a4779-7218-418e-924f-909b99eb7227
Continuous Symmetries, Lie Algebras, Differential Equations and Computer Algebra (2nd ed.)
Steeb, Willi-Hans
calibre (7.6.0) [https://calibre-ebook.com]
2007-06-20T02:54:11+00:00
<div><div class="review"> In the introduction, the author writes, "Continuous group theory, Lie
algebras and differential geometry play an important role in the
understanding of the structure of nonlinear partial differential
equations, in particular for generating integrable equations, finding
Lax pairs, recursion operators, Bäcklund transformations and finding
exact analytical solutions.'' This book provides a self-contained and
very accessible introduction to these topics.
<br>
The book begins with basic material on Lie groups, Lie algebras, group
actions and their infinitesimal generators, differential forms and
tensors. Examples arising from symmetry groups of some elementary
differential equations and from the study of invariant and conformally
invariant tensors are given. The author then does a nice job of
describing the basic techniques for finding the Lie algebra of
infinitesimal symmetries for a system of differential equations, and
conversely, for finding those differential equations with a prescribed
group of symmetries. A list of some standard differential equations
and their symmetries is given. The book concludes with an introduction
to a variety of topics of current interest in the theory of integrable
systems: Lie-Bäcklund or generalized symmetries; recursion
operators; Lax representations; conservation laws; and Painlevé
tests. None of these topics are dealt with in great detail or with a
great amount of rigor, but nevertheless this text, by consistently
presenting well-worked-out examples of all the main definitions,
provides a good starting point for anyone seeking a quick
introduction to these subjects. A novel feature of the text is the
inclusion of computer algebra routines, written in REDUCE, at the end
of each chapter.
</div>
<span class="ReviewedBy">Reviewed by <a href="http://ams.rice.edu/mathscinet/search/author.html?mrauthid=25810">Ian M. Anderson</a></span></div>
World Scientific
700962432
9810228910
eng
Differential equations
Partial Differential equations
Lie algebras
Continuous groups
mathematical physics
Lie theory