Group Analysis of One-Dimensional Gas Dynamics Equations in Lagrangian Coordinates and Conservation Laws
C. Kaewmanee1, S. V. Meleshko2
1Naresuan University, Phitsanulok, 65000, Thailand
2Suranaree University of Technology, Nakhon Ratchasima, 30000, Thailand
Keywords: групповой анализ, уравнения газовой динамики, лагранжевы координаты, групповая классификация, законы сохранения, group analysis, gas dynamics equations, Lagrangian coordinates, group classification, conservation laws
Abstract
A group analysis of the second-order equation including one-dimensional gas dynamics equations in Lagrangian coordinates as a particular case is performed. The use of Lagrangian coordinates makes it possible to consider one-dimensional gas dynamics equations as a variational Euler-Lagrange equation with an appropriate Lagrangian. Conservation laws are derived with the use of the variational presentation and Noether theory. A complete group classification of the Euler-Lagrange equation is obtained; as a result, 18 different classes can be classified.
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