Inverse Scattering Problem for Vector Fields and the Heavenly Equation

Details Inverse Scattering Problem for Vector Fields and the Heavenly Equation Inverse Scattering Problem for Vector Fields and the Heavenly Equation

2005-12-16

arxiv.org/abs/nlin/0512043v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

18 pages

Scientific paper

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

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