Group classification of one equations that arised when describing one-dimensional gas motions

Viktor K. Andreev

Institute of Computational Modelling SB RAS, Krasnoyarsk, Russian Federation

Abstract: The results of solving the group classification problem of a universal nonlinear equation of one-dimensional gas flows with plane, cylindrical and spherical waves are presented. All specializations of the state equation are found when the main group is expanded. In particular, in the case of plane waves, in addition to the known ones, a polytropic gas with an adiabatic index of $\gamma=5$ is released.

Keywords: equations of one-dimensional gas dynamics, Lagrangian variables, Lie group generators, state equations, group classification.

UDC: 517.9

Received: 10.03.2024
Received in revised form: 13.01.2025
Accepted: 04.06.2025

Language: English