New Applications of a Kind of Infinitesimal-Operator Lie Algebra

Abstract EN

Applying some reduced Lie algebras of Lie symmetry operators of a Lie transformation group, we obtain an invariant of a second-order differential equation which can be generated by a Euler-Lagrange formulism.

A corresponding discrete equation approximating it is given as well.

Finally, we make use of the Lie algebras to generate some new integrable systems including ( 1 + 1 ) and ( 2 + 1 ) dimensions.