The Hamiltonian Field Theory of the Von Mises Wave Equation: Analytical and Computational Issues (Communications in Computational Physics, 2018)
The Von Mises quasi-linear second order wave equation, which completelydescribes an irrotational, compressible and barotropic classical perfect fluid, can be derivedfrom a nontrivial least action principle for the velocity scalar potential only, incontrast to existing analog formulations which are expressed in terms of coupled densityand velocity fields. In this article, the classical Hamiltonian field theory specificallyassociated to such an equation is developed in the polytropic case and numericallyverified in a simplified situation. The existence of such a mathematical structure suggestsnew theoretical schemes possibly useful for performing numerical integrations offluid dynamical equations. Moreover, it justifies possible new functional forms for Lagrangiandensities and associated Hamiltonian functions in other theoretical classicalphysics contexts.