Comment on “Generalized W∞ symmetry algebra of the conditionally integrable nonlinear evolution equation” [J. Math. Phys. 36, 3492 (1995)]

Two remarks on an inverse operator of a differential operator ∂x and on symmetries of two kinds of differential equations Δ(u)=0 and ∂xΔ(u)=0 are pointed out and then a few of remarks about the paper “Generalized W∞ symmetry algebra of the conditionally integrable nonlinear evolution equation” [Y. Lou and J. P. Weng, J. Math. Phys. 36, 3492 (1995)] are presented. It is in particular shown that if we consider ∂x−1 to be a linear and right inverse operator of ∂x, the vector fields σnu(f ) proposed in the above paper are not certain to be symmetries of the Jimbo–Miwa–Kadomtsev–Petviashvili system under consideration. Moreover the commutators of a generalized W∞ algebra established among these vector fields do not always hold. Therefore the vector fields σnu(f ) do not provide an example of application of the formal series ansatz in the above paper.