Abstract
In this paper, three-mode nonlinear coherent states are introduced by using the complex solution of the equation q3 = 1. The photon-added or photon-subtracted three-mode nonlinear coherent states are shown to be three-mode nonlinear coherent states with different nonlinear functions. The Z3-graded parity coherent states are introduced as examples of three-mode nonlinear coherent states. Finally, multi-mode coherent states and multi-mode nonlinear coherent states are also constructed in a similar way.
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