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Mathematics
In this report we describe the generalization of Darboux method for systems of partial differential equations. The approach is based on using the invariants of characteristics. The equations of gas dynamics are considered as applications. For special state equation we obtained the exact solution by using zero order invariants. This solution depends on two arbitrary functions. We also obtained the form of a speed sound function, for which the first order invariants exist. Using these invariants we reduced the system of gas dynamics equations to a couple of ordinary differential equations.
This work was supported in part by the Russian Foundation for Basic Research (the grant 04-01-00130).
Note. Abstracts are published in author's edition
Last update: 06-Jul-2012 (11:52:45)