Higher-order SUSY, linearized nonlinear Heisenberg algebras and coherent states

Using an iterative construction of the first-order intertwining technique, we find k-parametric families of exactly solvable anharmonic oscillators wh ose spectra consist of-a part isospectral to the oscillator plus k addition al levels at arbitrary positions below E-0 = 1/2. It is seen that the 'natu ral' ladder operators for these systems give place to polynomial nonlinear algebras, and it is shown that these algebras can be linearized. The cohere nt states construction is performed in the nonlinear and linearized cases.