Classification of conservation laws for KdV--like equations

We prove that the computation of the conservation laws of (2n + 1)th-order KdV-like equations (i.e. higher order evolution equations with the same scaling as KdV) can be restricted to polynomials with constant terms, except when the order of the conservation law equals n - 1, in which case the density has linear t dependence. This shows that existing computer algebra programs which assume the conservation law to be of this form are providing the complete answer