On the constrained \(q\)-mKP hierarchy: Additional symmetry and a hidden Virasoro algebraic structure

We construct the additional symmetry of the constrained \(q\) -mKP hierarchy. The new modified operator is introduced. The flows and additional flows acting on the modified operator are given. The additional flows acting on the eigenfunction and the adjoint eigenfunction are presented. The hidden Virasoro algebraic structure in the additional symmetry of the constrained \(q\) -mKP hierarchy is given.