  We propose the Hirota bilinearization of the Fokas-Lenells derivative
nonlinear Schrodinger equation with a non-vanishing background. The bilinear
method is applied using an auxilary function to obtain the dark one soliton
solution, dark two soliton solution and eventually the scheme for obtaining
dark N soliton solutions. The use of auxilary function in bilinearization makes
the method simpler than the ones reported earlier. Later, we have introduced a
Lax pair for this integrable equation and using a transformation we have shown
that this system is gauge equivalent to a spin system, namely the
Landau-Lifshitz equation.
