Integrability conditions for systems of two equations of the form u /sub t/ = A(u)u /sub xx/ + F(u, u /sub x/)

This paper finds necessary conditions for the existence of nontrivial conservation laws for systems of nonlinear equations. The equations take the form of densities of local conservation laws constructed in a definite manner from the coefficients of the system. The conditions can be readily verified in each specific case. A module of simple invertible substitutions that makes it possible to reduce the system to a canonical form when some integrability conditions are satisfied is discussed