  We study local conservation laws for evolution equations in two independent
variables. In particular, we present normal forms for the equations admitting
one or two low-order conservation laws. Examples include Harry Dym equation,
Korteweg-de-Vries-type equations, and Schwarzian KdV equation. It is also shown
that for linear evolution equations all their conservation laws are (modulo
trivial conserved vectors) at most quadratic in the dependent variable and its
derivatives.
