Computation of the Lie-Bäcklund algebras for second-order equations (Q802084)

A method of calculating Lie-Bäcklund algebras is given for a second- order equation with two independent variables. For that purpose a criterion for the computation of the mixed derivatives from a system obtained by differentiation from the original equation is derived. The equations defining the algebra are analysed when the criterion is satisfied. A class of equations with the maximal algebra is given. As examples, the equation of developable surfaces and a quasilinear equation are considered.