The four-dimensional Martinez 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.

References in corpus (2)

• The four-dimensional Martinez Alonso--Shabat equation: reductions and nonlocal symmetries
• Higher symmetries of cotangent coverings for Lax-integrable multi-dimensional partial differential equations and Lagrangian deformations

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• Lax representations with non-removable parameters and integrable hierarchies of PDEs via exotic cohomology of symmetry algebras
• Recursion Operators for Multidimensional Integrable PDEs
• Integrability of S-deformable surfaces: conservation laws, Hamiltonian structures and more
• Group interpretation of the spectral parameter. The case of isothermic surfaces
• On the algebra of nonlocal symmetries for the 4D Mart\'ınez Alonso-Shabat equation