  In preprint we consider and compare different definitions of generalized
solution of the Cauchy problem for 1d-scalar quasilinear equation (conservation
law). We start from the classical approaches goes back to I.M. Gelfand, O.A.
Oleinik, S.N. Kruzhkov and move to the modern finite-difference approximations
approaches belongs to A.A. Shananin and G.M. Henkin. We discuss the conditions
that provide definitions to be equivalent.
