A class of Einstein--Weyl spaces associated to an integrable system of hydrodynamic type

Abstract

HyperCR Einstein--Weyl equations in 2+1 dimensions reduce to a pair of quasi-linear PDEs of hydrodynamic type. All solutions to this hydrodynamic system can be in principle constructed from a twistor correspondence, thus establishing the integrability. Simple examples of solutions including the hydrodynamic reductions yield new Einstein--Weyl structures.

Final version. To appear in JGP

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Cited by in corpus (54)

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• On the dbar-dressing method applicable to heavenly equation
• Classical R-matrix theory for bi-Hamiltonian field systems
• Einstein--Weyl geometry, dispersionless Hirota equation and Veronese webs
• Symmetry reductions and exact solutions of Lax integrable $3$-dimensional systems
• The Inverse Spectral Transform for the Dunajski hierarchy and some of its reductions, I: Cauchy problem and longtime behavior of solutions
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• Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking
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• On the heavenly equation hierarchy and its reductions
• Nonlocal symmetries, conservation laws, and recursion operators of the Veronese web equation
• On a class of 2D integrable lattice equations
• A Two-Component Generalization of the Integrable rdDym Equation
• Integrable dispersionless PDEs arising as commutation condition of pairs of vector fields
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• A construction of Einstein-Weyl spaces via LeBrun-Mason type twistor correspondence
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• Higher symmetries of cotangent coverings for Lax-integrable multi-dimensional partial differential equations and Lagrangian deformations
• Multidimensional integrable systems and deformations of Lie algebra homomorphisms
• Lax representations with non-removable parameters and integrable hierarchies of PDEs via exotic cohomology of symmetry algebras
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• Second-order PDEs in 3D with Einstein-Weyl conformal structure
• Point invariants of third-order ODEs and hyper-CR Einstein-Weyl structures
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• On the relationship between nonlinear equations integrable by the method of characteristics and equations associated with commuting vector fields
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• A note on the Hyper--CR equation, and gauged $N=2$ supergravity
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• A Covering for the dKP-hyper CR Interpolating Equation and Multi-Valued Einstein-Weyl Structures
• On linear degeneracy of integrable quasilinear systems in higher dimensions
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• From the conformal self-duality equations to the Manakov-Santini system
• The Cauchy problem for the Pavlov equation with large data
• The twistor theory of Whitham hierarchy
• Recursion operators in the cotangent covering of the rdDym equation