Equivalence groups for balance equations of arbitrary order―Part Ⅰ

摘要

The groups of equivalence transformations for a family of balance equations of arbitrary order involving arbitrary number of independent and dependent variables are investigated. Equivalence groups are essentially much more general than symmetry groups in the sense that they map equations containing arbitrary functions or parameters onto equations of the same structure but with different functions or parameters. We attack the problem of determination of group structure of a system of arbitrary balance equations through exterior calculus. The analysis is reduced to determine isovector fields of a closed ideal of an exterior algebra over an appropriate differentiable manifold dictated by the structure of the differential equations by employing almost solely algebraic operations. The isovector fields induce point transformations, which are none other than the desired equivalence transformations, generated by their orbits which leave that particular ideal invariant. The determining equations are fully obtained. It is shown that symmetry transformations can also be deduced directly from equivalence transformations.