Inverse Scattering Problem for Vector Fields and the Heavenly Equation

Abstract

We solve the inverse scattering problem for multidimensional vector fields and we use this result to construct the formal solution of the Cauchy problem for the second heavenly equation of Plebanski, a scalar partial differential equation in four dimensions relevant in General Relativity, which arises from the commutation of multidimensional Hamiltonian vector fields

18 pages

References in corpus (1)

• A hodograph transformation which applies to the heavenly equation

Cited by in corpus (10)

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• Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking
• Nonlocality and the inverse scattering transform for the Pavlov equation
• Partially integrable systems in multidimensions by a variant of the dressing method. 1
• An integral geometry lemma and its applications: the nonlocality of the Pavlov equation and a tomographic problem with opaque parabolic objects
• The Cauchy problem for the Pavlov equation
• The Cauchy problem for the Pavlov equation with large data