Regular and nonregular partially invariant solutions (Q1363839)

The aim of this work is to substantiate the appropriateness of introducing a new classification feature for partially invariant solutions of differential equations. After explaining the general situation, we describe a system of equations of gas dynamics and point out possible classes of partially invariant solutions with respect to admissible three-dimensional subgroups. Specific examples of regular and nonregular solutions that clearly demonstrate the important differences between these solutions are discussed.