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.
Categories: math.DG math-ph math.MP