Group classification of Rapoport–Leas equations

Abstract

In this work we study the so-called Rapoport–Leas equations using methods of differential invariants and geometric theory of differential equations. Such equations are very important for the problems of non-linear filtration and for the problems of oil extraction. We calculate symmetry algebras for the different classes of Rapoport–Leas equations and describe the algebras of differential invariants for the actions of symmetry algebras on the solutions of Rapoport–Leas equations.