Equations of Hydrodynamic Type

Abstract

The universal field equations introduced by the author and his collaborators, which admit infinitely many inequivalent Lagrangian formulations are shown to arise as consistency conditions for the existence of non-trivial solutions to the quasi-linear equations, called equations of hydrodynamic type by Novikov , Dubrovin and others. The solutions in closed form are only implicit. A method due to Stokes, which is in essence just Fourier Analysis is resurrected for application to those equations. With the benefit of algebraic computation facilities, this method, allows the general structure of power series solutions to be conjectured.