Interpolating Dispersionless Integrable System

Abstract

We introduce a dispersionless integrable system which interpolates between the dispersionless Kadomtsev-Petviashvili equation and the hyper-CR equation. The interpolating system arises as a symmetry reduction of the anti--self--dual Einstein equations in (2, 2) signature by a conformal Killing vector whose self--dual derivative is null. It also arises as a special case of the Manakov-Santini integrable system. We discuss the corresponding Einstein--Weyl structures.

11 pages. New title, some errors corrected, section 5 removed. Final version, to appear in J. Phys. A

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Cited by in corpus (14)

• Darboux transformation of the generalized coupled dispersionless integrable system
• On the Einstein-Weyl and conformal self-duality equations
• Central extensions of cotangent universal hierarchy: (2+1)-dimensional bi-Hamiltonian systems
• Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking
• `Interpolating' differential reductions of multidimensional integrable hierarchies
• An action principle for the Einstein-Weyl equations
• Non-Hamiltonian generalizations of the dispersionless 2DTL hierarchy
• On a class of reductions of Manakov-Santini hierarchy connected with the interpolating system
• Twistor Theory and Differential Equations
• Second-order PDEs in 3D with Einstein-Weyl conformal structure
• Dunajski-Tod equation and reductions of the generalized dispersionless 2DTL hierarchy
• Matrix extension of the Manakov-Santini system and integrable chiral model on Einstein-Weyl background
• Proper conformal symmetries in SD Einstein spaces
• From the conformal self-duality equations to the Manakov-Santini system