  We determine the low-energy spectrum and the eigenstates for a two-bosonic
mode nonlinear model by applying the In\"{o}n\"{u}-Wigner contraction method to
the Hamiltonian algebra. This model is known to well represent a Bose-Einstein
condensate rotating in a thin torus endowed with two angular-momentum modes as
well as a condensate in a double-well potential characterized by two space
modes. We consider such a model in the presence of both an attractive and a
repulsive boson interaction and investigate regimes corresponding to different
values of the inter-mode tunneling parameter. We show that the results ensuing
from our approach are in many cases extremely satisfactory. To this end we
compare our results with the ground state obtained both numerically and within
a standard semiclassical approximation based on su(2) coherent states.
