TY - JOUR
T1 - The Hamiltonian Field Theory of the Von Mises Wave Equation: Analytical and Computational Issues
AU - Christian Cherubini & Simonetta Filippi
JO - Communications in Computational Physics
VL - 3
SP - 758
EP - 769
PY - 2018
DA - 2018/04
SN - 19
DO - http://doi.org/10.4208/cicp.101114.140715a
UR - https://global-sci.org/intro/article_detail/cicp/11108.html
KW - 
AB - <p style="text-align: justify;">The Von Mises quasi-linear second order wave equation, which completely
describes an irrotational, compressible and barotropic classical perfect fluid, can be derived
from a nontrivial least action principle for the velocity scalar potential only, in
contrast to existing analog formulations which are expressed in terms of coupled density
and velocity fields. In this article, the classical Hamiltonian field theory specifically
associated to such an equation is developed in the polytropic case and numerically
verified in a simplified situation. The existence of such a mathematical structure suggests
new theoretical schemes possibly useful for performing numerical integrations of
fluid dynamical equations. Moreover, it justifies possible new functional forms for Lagrangian
densities and associated Hamiltonian functions in other theoretical classical
physics contexts.</p>