Vishik equivalence and similarity of quasilinear p-forms and totally singular quadratic forms

For quadratic forms over fields of characteristic different from two, there is a so-called Vishik criterion, giving a purely algebraic characterization of when two quadratic forms are motivically equivalent.In analogy to that, we define Vishik equivalence on quasiliner p-forms.We study the question whether Vishik equivalent p-forms must be similiar.We prove that this is not true for quasilinear p-forms in general, but we find some families of totally singular quadratic forms (i.e., of quasilinear 2-forms) for which the question has positive answer.