Virasoro symmetry of constrained KP hierarchies |
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| Institution: | 1. Department of Physics, University of Illinois at Chicago, 845 W. Taylor Street, Chicago, IL 60607-7059, USA;2. Institute of Nuclear Research and Nuclear Energy, Boul. Tsarigradsko Chausee 72, BG-1784 Sofia, Bulgaria;3. Department of Physics, Ben-Gurion University of the Negev, Box 653, IL-84105 Beer Sheva, Israel;1. Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China;2. Department of Physics, Hangzhou Normal University, Hangzhou 310036, China;3. Faculty of Science, Ningbo University, Ningbo 315211, China;4. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai 200062, China;5. Institute of Systems Science, East China Normal University, Shanghai 200241, China;1. Acibadem University, School of Medicine, Department of Otolaryngology, Head and Neck Surgery, Istanbul, Turkey;2. Sisli Hamidiye Etfal Education and Research Hospital, Department of Otolaryngology, Istanbul, Turkey;3. Hopa State Hospital, Department of Otolaryngology, Artvin, Turkey |
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| Abstract: | The conventional formulation of additional nonisospectral sysmmetries for the full Kadomtsev-Petviashvili (KP) integrable hierarchy is not compatible with the reduction to the important class of constrained KP (cKP) integrable models. This paper solves explicitly the problem of compatibility of the Virasoro part of additional symmetries with the underlying constraints of cKP hierarchies. Our construction involves an appropriate modification of the standard additional-symmetry flows by adding a set of “ghost symmetry” flows. We also discuss the special case of cKP — truncated KP hierarchies, obtained as Darboux-Bäcklund orbits of initial purely differential Lax operators. Our construction establishes the condition for commutativity of the additional-symmetry flows with the discrete Darboux-Bäcklund transformations of cKP hierarchies leading to a new derivation of the string-equation constraint in matrix models. |
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