Local conservation laws of second-order evolution equations

Generalizing results by Bryant and Griffiths (1995 Duke Math. J. 78 531), we completely describe local conservation laws of second-order (1 + 1)-dimensional evolution equations up to contact equivalence. The possible dimensions of spaces of conservation laws prove to be 0, 1, 2 and infinity. The canonical forms of equations with respect to contact equivalence are found for all nonzero dimensions of spaces of conservation laws. (fast track communication)