A hierarchy of integrable PDEs in 2+1 dimensions associated with 2 -   dimensional vector fields
  We introduce a hierarchy of integrable PDEs in 2+1 dimensions arising from the commutation of 2-dimensional vector fields. We also solve the associated Cauchy problems, using the recently developed Inverse Scattering Transform for 1-parameter families of multidimensional vector fields. 
S. V. Manakov and P. M. Santini