Inverse Scattering Problem for Vector Fields and the Cauchy Problem for the Heavenly Equation
Exactly Solvable and Integrable Systems
2009-11-11 v1
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.
Cite
@article{arxiv.nlin/0604024,
title = {Inverse Scattering Problem for Vector Fields and the Cauchy Problem for the Heavenly Equation},
author = {S. V. Manakov and P. M. Santini},
journal= {arXiv preprint arXiv:nlin/0604024},
year = {2009}
}
Comments
15 pages, submitted to Phisics Letters A. This paper replaces nlin.SI/0512043