Response to “Comment on ‘Generalized W∞ symmetry algebra of the conditionally integrable nonlinear evolution equation’ ” [J. Math. Phys. 40, 3685 (1999)

Abstract

To verify the correctness of the high order symmetries for the Jimbo–Miwa–Kadomtsev–Petviashvilli system (JMKP) and the potential JMKP (PJMKP) system given in our paper [J. Math. Phys. 36, 3492–3497 (1995)], Ma’s definition of ∂x−1 may be used only for the general nonkernel solutions of the models. For some types of special solutions which are the kernels of some differential operators, one has to use ∂x−1 as the indefinite operator and selected the integral functions appropriately.