The general method of obtaining conservation laws for (non-linear) partial differential equations (PDE's) introduced by A. Pr\'astaro and another one by A. M. Vinogradov, are considered and the general covariance of such methods is studied. In particular, it is shown that Vinogradov's method fails to be fully covariant in the non-linear case. The relations between the number of conservation laws for PDEs and the Atiyah-Singer index theorem are studied. A criterion for recognize the wholly cohomological character of a PDE is given and the link between spectral sequences and wholly cohomlogical equations is found. Some examples of interesting PDEs which arise in physics are also considered.
On the conservation laws of PDE's / Marino, V; Prastaro, Agostino. - In: REPORTS ON MATHEMATICAL PHYSICS. - ISSN 0034-4877. - STAMPA. - 2:26(1988), pp. 211-225. [10.1016/0034-4877(88)90024-9]
On the conservation laws of PDE's.
PRASTARO, Agostino
1988
Abstract
The general method of obtaining conservation laws for (non-linear) partial differential equations (PDE's) introduced by A. Pr\'astaro and another one by A. M. Vinogradov, are considered and the general covariance of such methods is studied. In particular, it is shown that Vinogradov's method fails to be fully covariant in the non-linear case. The relations between the number of conservation laws for PDEs and the Atiyah-Singer index theorem are studied. A criterion for recognize the wholly cohomological character of a PDE is given and the link between spectral sequences and wholly cohomlogical equations is found. Some examples of interesting PDEs which arise in physics are also considered.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
