The four-dimensional Martínez Alonso–Shabat equation: Differential coverings and recursion operators

Abstract

We apply Cartan's method of equivalence to find a contact integrable extension for the structure equations of the symmetry pseudo-group of the four-dimensional Martinez Alonso - Shabat equation. From the extension we derive two differential coverings including coverings with one and two non-removable parameters. Then we apply the same approach to construct a recursion operator for symmetries of the equation under study.