Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation |
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| Affiliation: | 1. Landau Institute for Theoretical Physics, Moscow, Russia;2. Dipartimento di Fisica, Università di Roma “La Sapienza”, and Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Piazz.le Aldo Moro 2, I-00185 Roma, Italy |
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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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