Soliton pulse compression in a dispersion decreasing elliptic birefringent fiber with effective gain and effective phase modulation

We have considered soliton pulse compression in a dispersion decreasing ideal elliptical birefringent fiber with phase modulation. We have shown that there is exact balancing between the effective gain and the effective phase modulation and as a result arrive at the fundamental soliton solution. For the various dispersion decreasing profiles we have considered, we have shown that the hyperbolic profile is the best suitable choice for the dispersion decreasing profile as it provides fairly good compression even after compensating for the fiber loss.