Abstract
In this paper, we construct Virasoro-type additional symmetry of the constrained multi-component q -deformed KP ( q -KP) hierarchy, which is obtained as particular reduction imposed on the multi-component q -KP hierarchy. Then the investigation of the multi-component q -deformed modified KP ( q -mKP) hierarchy and its additional symmetry is given as well. Furthermore, the Virasoro-type additional symmetry and the corresponding algebraic structure in the constrained case are also considered.
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