Recursion operators for dispersionless integrable systems in any dimension

Abstract

We present a new approach to construction of recursion operators for multidimensional integrable systems which have a Lax-type representation in terms of a pair of commuting vector fields. It is illustrated by the examples of the Manakov--Santini system which is a hyperbolic system in N dependent and N + 4 independent variables, where N is an arbitrary natural number, the six-dimensional generalization of the first heavenly equation, the modified heavenly equation, and the dispersionless Hirota equation.

revised version (introduction, section 5, and bibliography expanded), 10 pages, LaTeX, no figures

References in corpus (8)

• Inverse Scattering Problem for Vector Fields and the Cauchy Problem for the Heavenly Equation
• On the integrability of symplectic Monge-Ampére equations
• On the structure of $(2+1)$--dimensional commutative and noncommutative integrable equations
• On the heavenly equation hierarchy and its reductions
• Bi-Hamiltonian representation, symmetries and integrals of mixed heavenly and Husain systems
• On a class of second-order PDEs admitting partner symmetries
• Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions
• Recursion operator for the IGSG equation

Cited by in corpus (13)

• A Simple Construction of Recursion Operators for Multidimensional Dispersionless Integrable Systems
• The four-dimensional Martinez Alonso--Shabat equation: reductions and nonlocal symmetries
• Integrable dispersionless PDE in 4D, their symmetry pseudogroups and deformations
• Einstein--Weyl geometry, dispersionless Hirota equation and Veronese webs
• On a method for constructing the Lax pairs for nonlinear integrable equations
• Symmetries and conservation laws for the Karczewska--Rozmej--Rutkowski--Infeld equation
• Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation
• Integrable dispersionless PDEs arising as commutation condition of pairs of vector fields
• Higher symmetries of cotangent coverings for Lax-integrable multi-dimensional partial differential equations and Lagrangian deformations
• Dispersionless (3+1)-dimensional integrable hierarchies
• Six-dimensional heavenly equation. Dressing scheme and the hierarchy
• Integrability of S-deformable surfaces: conservation laws, Hamiltonian structures and more
• On nonlocal symmetries for the Krichever--Novikov equation