  The paper proves that any asymptotically shearfree congruence at the
conformal infinity (scri) in a (2,2)-signature spacetime is determined locally
by a solution to the pair of forced inviscid Burgers' equations
L_u+LL_x={\sigma}(u,x,y,L) and M_u+MM_y={\sigma}'(u,x,y,M) where u,x,y are
Bondi coordinates of scri. The functions {\sigma} and {\sigma}' are determined
naturally by the projective structure on the {\alpha} and {\beta} surfaces that
foliate scri.
