Abstract

Some Generalizations for the Noether Theorem: Differential and Difference Equations

V.Dorodnitsyn (Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia)

e-mail: dorod@spp.keldysh.ru

It is known from the Noether theorem, that the invariance of variational functional with respect to r-parameter group leads to the existence of r conservation laws for corresponding Euler's equation. Meanwhile there exist r equations associated with Euler's equation which possess their own conservation laws. Some of such equations can be viewed as the Euler equations of variational functionals. Similar situation can observed for finite-difference equations. Several examples for ODEs and PDEs were considered.

Section : 12