Symmetries of the D$\Delta$mKP hierarchy and their continuum limits
2023
Online
report
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 Schr\"odinger 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.
Comment: 23 pages
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Symmetries of the D$\Delta$mKP hierarchy and their continuum limits
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Autor/in / Beteiligte Person: | Liu, Jin ; Zhang, Da-jun ; Zhao, Xuehui |
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Veröffentlichung: | 2023 |
Medientyp: | report |
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