Reductions of partially invariant solutions of rank 1 defect 2 five-dimensional overalgebra of conical subalgebra

Abstract

Conic flows are the invariant rank 1 solutions of the gasdynamics equations on the three-dimensional subalgebra defined by the rotation operators, translation by time and uniform dilatation. The generalization of the conic flows are partially invariant solutions of rank 1 defect 2 on the five-dimensional overalgebra of conic subalgebra extended by the operators of space translations noncommuting with rotation. We prove that that the extensions of conic flows are reduced either to function-invariant plane stationary solutions or to a double wave of isobaric motions or to the simple wave.