Internal symmetries and the conservation laws for the classical theory of a vector field of general type

A study is made of a six-parameter internal-symmetry group of the classical theory of a vector field of general type (and its nonlinear generalizations). This group, which is not related to a change of the space-time coordinates, is interpreted physically.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 77–81, April, 1978.We are sincerely grateful to F. I. Fedorov for interest in the work, and also to A. A. Bogush, L. F. Zhirkov, and E. A. Tolkachev for helpful and critical discussion of our results.