Solitons for nearly integrable bright spinor Bose-Einstein condensate

‎Using the explicit forms of eigenstates for linearized operator related to a matrix version of Nonlinear Schrödinger equation‎, ‎soliton perturbation theory is developed for the $F=1$ bright spinor Bose-Einstein condensates‎. ‎A small disturbance of the integrability condition can be considered as a small correction to the integrable equation‎. ‎By choosing appropriate perturbation‎, ‎the soliton solution for small deviation from the integrability condition is found‎. ‎Numerical simulations exhibit good agreement with analytical results.