Inverse Scattering Problem for Vector Fields and the Cauchy Problem for the Heavenly Equation
S. V. Manakov, P. M. Santini
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 relevant in General Relativity, which arises from the commutation of multidimensional Hamiltonian vector fields.
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