| Popis: |
Discussed is the problem of employing the group G, admitted (in the sense of S. Lie) by the given system of partial differential equations S for the construction of some classes of particular solutions of S. By means of each non-transitive subgroup H ⊂ G the so-called partly invariant H-solutions are constructed. The classification of partly invariant solutions is based upon two characteristic integers: the rank and the defect of invariance. The application of these concepts is demonstrated on the example of “double wave” type solutions of the gas dynamics equations. Particularly a theorem is communicated that in some sense each “double wave” is an isentropic one. |
