Lie symmetry analysis of differential equations provides a powerful and fundamental
framework to the exploitation of systematic procedures leading to the integration by …

Through the previous three editions, Handbook of Differential Equations has proven an
invaluable reference for anyone working within the field of mathematics, including …

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 …

I will sketchily illustrate how the theory of symmetry helps in determining solutions of
(deterministic) differential equations, both ODEs and PDEs, staying within the classical …

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 …

We show that an nth (n⩾ 3) order linear ordinary differential equation has exactly one of n+
1, n+ 2, or n+ 4 (the maximum) point symmetries. The Lie algebras corresponding to the …

ut= [r(u)uxlx + [+(u)], u,,=[K(u)u,]x. u* = u + on(X, t, u), dx/~ = dt/~ = du/~. Vt= K(V~)V.:x + q~(Vx)
V,=K(V.)Vx Page 1 Volume 118, number 4 PHYSICS LETTERS A 13 October 1986 SOME …

A complete group classification is given of both the wave equation c 2 (x) uxx− utt= 0 (I) and
its equivalent system vt= ux, c 2 (x) vx= ut (II) when the wave speed c (x)≠ const. Equations …

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 …