This book is a significant update of the first four chapters of Symmetries and Differential
Equations (1989; reprinted with corrections, 1996), by George W. Bluman and Sukeyuki …

The direct method for the construction of local conservation laws of partial differential
equations (PDE) is a systematic method applicable to a wide class of PDE systems (S. Anco …

by spin or (spin s= 1/2) field equations is emphasized because their solutions can be used
for constructing solutions of other field equations insofar as fields with any spin may be …

New classes of symmetries for partial differential equations are introduced. By writing a
given partial differential equation S in a conserved form, a related system T with potentials …

A self-contained introduction to the methods and techniques of symmetry analysis used to
solve ODEs and PDEs Symmetry Analysis of Differential Equations: An Introduction presents …

Overall, our object has been to provide an applications-oriented text that is reasonably self-
contained. It has been used as the basis for a graduate-level course both at the University of …

In this paper we discuss symmetry reductions and exact solutions of the Boussinesq
equation using the classical Lie method of infinitesimals, the direct method due to Clarkson …

The study of (nonlinear) dift" erential equations was S. Lie's motivation when he created
what is now known as Lie groups and Lie algebras; nevertheless, although Lie group and …

We consider classes C of differential equations characterized by the presence of arbitrary
elements, that is, arbitrary functions or constants. Based on an idea of Ovsiannikov, we …

Nonlinearity plays a major role in the understanding of most physical, chemical, biological,
and engineering sciences. Nonlinear problems fascinate scientists and engineers, but often …