In this paper, we consider the pulse propagation through the birefringent fiber with linear coupling effects. Using the Stokes parameter formalism and conserved densities, we construct the undamped Duffing oscillator equation from integro-differential equations. We also discuss the variation of potential well for different choices of physical parameters. From the linear stability analysis and numerical methods, we also discuss the stability, instability and bifurcation phenomenon in the birefringent fiber through Duffing oscillator type equation.