Nonlinear Squeezed States and Multiplication Rule of Nonlinear Squeezing Operators Gained via Nonlinear Coherent State Representation and IWOP Technique

Using the nonlinear coherent state representation we derive nonlinearsqueezed states and the multiplication rule of nonlinear squeezingoperators. We find that the symplectic matrices multiplication rule innonlinear coherent state projection operator representation maps into themultiplication rule of successive nonlinear squeezing operators. Thetechnique of integral within an ordered product of operators plays anessential role in deriving the multiplication rule.