Lax Triad Approach to Symmetries of Scalar Modified Kadomtsev–Petviashvili Hierarchy*

Abstract By means of Lax triads we reconstruct isospectral and nonisospectral scalar modified Kadomtsev–Petviashvili (mKP) hierarchies. In this approach the argument y is treated as an independent variable which is independent of time parameters { t 1 , t 2 , … } . Consequently, the isospectral and nonisospectral scalar mKP flows can have clear zero curvature representations, which enables us to handle investigation of symmetries of the scalar isospectral mKP hierarchy as freely as for (1+1)-dimensional systems. As a result, we obtain Lie algebraic structures of the scalar mKP flows and construct symmetries for the scalar isospectral mKP hierarchy.