Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation

S.V Manakov,P.M Santini

doi:10.1016/j.physleta.2006.07.011

Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation

S.V Manakov, P.M Santini

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https://doi.org/10.1016/j.physleta.2006.07.011

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Journal: Physics Letters A	Publication Date: Jul 18, 2006
Citations: 86

Affiliation: Landau Institute for Theoretical Physics, National Institute for Nuclear Physics

#Problem For Vector Fields #Multidimensional Vector Fields + Show 8 more

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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 nonlinear partial differential equation in four dimensions underlying self-dual vacuum solutions of the Einstein equations, which arises from the commutation of multidimensional Hamiltonian vector fields.

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