Noether’s theorems and systems of Cauchy-Kovalevskaya type. (English) Zbl 0656.58039

Olver, P. J.

Nonlinear systems of partial differential equations in applied mathematics, Proc. SIAM-AMS Summer Semin., Santa Fe/N.M. 1984, Lect. Appl. Math. 23, Pt. 2, 81-104 (1986).

[For the entire collection see Zbl 0579.00008.]
A. M. Vinogradov’s refinement of E. Noether’s theorems relating symmetries and conservation laws [J. Math. Anal. Appl. 100, 1-40; 41-129 (1984; Zbl 0548.58014; Zbl 0548.58015)] is discussed. Special attention is paid to the notion of a trivial conservation law as well as to the case of underdetermined and overdetermined systems. Simpler proofs of Vinogradov’s results are promised to appear in the author’s book “Applications of Lie groups to differential equations” (1986; Zbl 0588.22001).

Reviewer: S.V.Duzhin

MSC:

58J70

Invariance and symmetry properties for PDEs on manifolds

Keywords:

E. Noether’s theorems; symmetries; conservation laws; Lie groups

Citations:

Zbl 0579.00008; Zbl 0548.58014; Zbl 0548.58015; Zbl 0588.22001