Nonclassical symmetry analysis for hyperbolic partial differential equation

We consider the nonclassical symmetry of one-dimensional hyperbolic differential equations of the form ut + M(u)ux = 0. For the infinitesimal generator V = τ ∂ t + ξ ∂ x + ∑ i = 1 n ϕ i ∂ u i , it is shown that ξ is an eigenvalue of the matrix M when ϕi = 0 [Souichi M. Nonclassical symmetry and Riemann invariants. Int J Nonlinear Mech, [in press]]. In this paper, we prove a sufficient condition of a lemma.