Applications of Lie Groups to Differential Equations

The significance of symmetry methods has long been recognized for studying the differential equations arising in mathematics, physics, engineering, and many other disciplines. The purpose of this book is to provide a solid introduction to those applications of Lie groups to differential equations which have proved to be useful in practice, including determination of symmetry groups, integration of ordinary differential equations, construction of group-invariant solutions to partial differential equations, symmetries and conservation laws, generalized symmetries, and symmetry methods in Hamiltonian systems. Following an exposition of the applications, the book develops the underlying theory. The computational methods are presented such that graduate students and researchers in other fields can readily learn to use them. Many of the topics are discussed in a novel way, with an emphasis on explicit examples and computations. Further examples, as well as new theoretical developments appear in the exercises at the end of each chapter.