A Simple Construction of Recursion Operators for Multidimensional Dispersionless Integrable Systems

Abstract

We present a simple novel construction of recursion operators for integrable multidimensional dispersionless systems that admit a Lax pair whose operators are linear in the spectral parameter and do not involve the derivatives with respect to the latter. New examples of recursion operators obtained using our technique include {\em inter alia} those for the general heavenly equation, which describes a class of anti-self-dual solutions of the vacuum Einstein equations, and a six-dimensional equation resulting from a system of Ferapontov and Khusnutdinova.

14 p., no figures, significant revision

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• Recursion Operators and Tri-Hamiltonian Structure of the First Heavenly Equation of Plebański
• Nonlocal symmetries of Lax integrable equations: a comparative study
• Generalized symmetries, conservation laws and Hamiltonian structures of an isothermal no-slip drift flux model
• Generalized symmetries and conservation laws of (1+1)-dimensional Klein-Gordon equation
• Integrable (3+1)-dimensional system with an algebraic Lax pair
• Evolutionary Hirota Type (2+1)-Dimensional Equations: Lax Pairs, Recursion Operators and Bi-Hamiltonian Structures
• The integrable heavenly type equations and their Lie-algebraic structure
• Dispersionless (3+1)-dimensional integrable hierarchies
• Recursion operators and bi-Hamiltonian structure of the general heavenly equation
• Deforming Lie algebras to Frobenius integrable non-autonomous Hamiltonian systems
• Recursion Operators for Multidimensional Integrable PDEs
• Multidimensional integrable systems from contact geometry
• Lax pairs, recursion operators and bi-Hamiltonian representations of (3+1)-dimensional Hirota type equations
• Integrability of S-deformable surfaces: conservation laws, Hamiltonian structures and more
• Generalized symmetries of remarkable (1+2)-dimensional Fokker-Planck equation
• Formal recursion operators of integrable nonevolutionary equations and Lagrangian systems
• Bäcklund transformations as integrable discretization. The geometric approach
• Integrability of anti-self-dual vacuum Einstein equations with nonzero cosmological constant: an infinite hierarchy of nonlocal conservation laws
• Recursion operators in the cotangent covering of the rdDym equation
• Symmetry operators and generation of symmetry transformations of partial differential equations
• Recursion operators and bi-Hamiltonian representations of cubic evolutionary (2+1)-dimensional systems