Symmetries of the DΔmKP hierarchy and their continuum limits

In the recent paper [Stud. App. Math. 147 (2021), 752], squared eigenfunction symmetry constraint of the differential-difference modified Kadomtsev-Petviashvili (D Delta mKP) hierarchy converts the D Delta mKP system to the relativistic Toda spectral problem and its hierarchy. In this paper, we introduce a new formulation of independent variables in the squared eigenfunction symmetry constraint, under which the D Delta mKP system gives rise to the discrete spectral problem and a hierarchy of the differential-difference derivative nonlinear Schrodinger equation of the Chen-Lee-Liu type. In addition, by introducing nonisospectral flows, two sets of symmetries of the D Delta mKP hierarchy and their algebraic structure are obtained. We then present a unified continuum limit scheme, by which we achieve the correspondence of the mKP and the D Delta mKP hierarchies and their integrable structures.

Automated summary

This paper investigates the properties and transformations of the differential-difference modified Kadomtsev-Petviashvili (D Delta mKP) hierarchy. By introducing a new formulation of independent variables and nonisospectral flows, the paper obtains the discrete spectral problem of the hierarchy, a hierarchy of the differential-difference derivative nonlinear Schrödinger equation of the Chen-Lee-Liu type, and two sets of symmetries along with their algebraic structures. Finally, a unified continuum limit scheme is presented to establish the correspondence between the mKP hierarchy and the D Delta mKP hierarchy and their integrable structures.