On generalized Weber and Clebsch transformations

Abstract

Suitable generalizations of the Weber and Clebsch transformations of the hydrodynamic equations are introduced which have some bearing in the treatment of the inverse problem of Lagrangian field theory. In particular these generalizations open the way to equivalence proofs for several Lagrangians proposed in the realm of ideal (magneto-)hydrodynamics. This means that the Euler-Lagrange equations corresponding to these Lagrangians do not only imply but are also implied by the original field equations of the systems under study.