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

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

2006-04-11

arxiv.org/abs/nlin/0604024v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages, submitted to Phisics Letters A. This paper replaces nlin.SI/0512043

Scientific paper

10.1016/j.physleta.2006.07.011

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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