ARE SYMMETRY GROUPS OF PDE RESTRICTED BY THE JET BUNDLE FORMULATION?

Abstract

Yesl Any equation of conservation of the form ∂_x{P(∂_xφ, ∂_tφ) = ∂_t{Q(∂_xφ, ∂_tφ) is shown to admit an infinite-dimensional, Abellan group of symmetries that is not a prolongation symmetry group. Explicit equations are given for the determination of the generators of the Lle algebra of this Abellan symmetry group, and for the generators of Its underlying Poisson algebra.

1980 AMS Subject Classification:

• 58A3Ø
• 53B15