  A modal expansion approach is developed and employed to investigate and
elucidate the nonlinear mechanism behind the multistability and formation of
coupled multi-mode polariton solitons in microcavity wires. With pump switched
on and realistic dissipation parameters, truncating the expansion up to the
second-order wire mode, our model predicts two distinct coupled soliton
branches: stable and ustable. Modulational stability of the homogeneous
solution and soliton branches stability are studied. Our simplified 1D model is
in remarkably good agreement with the full 2D mean-field Gross-Pitaevskii
model, reproducing correctly the soliton existence domain upon variation of
pump amplitude and the onset of multistability.
