Inverse Scattering Problem for Vector Fields and the Heavenly Equation
  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 
S. V. Manakov and P. M. Santini