“…Modeling of nonlinear quantum optical physics phenomena (like, multimode radiation fields on multiphoton processes mediums, many -body physics models [1], [2], investigating the statistics of particles that interpolate between Bosons and Fermions, [13]- [17], or study of q-deformed oscillators [12], [16]) is expressed as Hamiltonians whose non-linearities are of higher order than the quadratic forms. In turn, such highly nonlinear Hamiltonians are associated with nonlinear q-deformed Lie algebra or polynomially deformed Lie algebras SU pd (2), [3].…”