Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation
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 selfdual vacuum solutions of the Einstein equations, which arises from the commutation of multidimensional Hamiltonian vector fields.
 Publication:

Physics Letters A
 Pub Date:
 December 2006
 DOI:
 10.1016/j.physleta.2006.07.011
 arXiv:
 arXiv:nlin/0604024
 Bibcode:
 2006PhLA..359..613M
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 15 pages, submitted to Phisics Letters A. This paper replaces nlin.SI/0512043