$sl(2)$ variational schemes for solving one class of quantum nonlinear models

Hamiltonians of a wide-spread class of $G_{inv}$-invariant nonlinear quantum models, including multiboson and frequency conversion ones, are expressed as non-linear functions of $sl(2)$ generators. It enables us to use standard variational schemes, based on $sl(2)$ generalized coherent states as trial functions, for solving both spectral and evolution tasks. In such a manner a new analytical expression is found for energy spectra in a mean-field approximation which is beyond quasi-equidistant ones obtained earlier.