Symmetry analysis of nonlinear differential equations with the ``Mathematica'' program SYMMAN (Q1368551)

The article discusses the determination and application of various generalizations of classical Lie symmetries like conditional or partial symmetries based on two examples: the nonlinear wave equation \(u_{tt}-(uu_x)_x=0\) and the family \(u_t=(k(u)u_x)_x+q(u)\) of nonlinear heat equations. The use of some Mathematica packages is mentioned, however no detailed description of them given. Most of the calculations are based on an earlier result of the author [Symmetries of compatibility conditions for overdetermined systems of differentiation equations, Acta Appl. Math. 26, 61-86 (1992; Zbl 0763.35013)] that the determining system for nonclassical symmetries inherits the classical symmetries of the original system.