Optical pulse propagation in inhomogeneous fibers in the anomalous dispersive regime: dispersion-managed bright solitons

We study the nonlinear electromagnetic wave propagation in inhomogeneous fibers in the anomalous dispersive regime. In order to include the inhomogeneous physical effects, the nonlinear Schrödinger (NLS) equation, which governs the solitary pulse propagation in optical fiber, is modified by adding terms for phase modulation and fiber power loss/gain. Lax pair construction and Hirota transformation are introduced in order to bilinearize and solve the modified inhomogeneous NLS equations. A general integrability condition is arrived for gain and loss cases. The modified NLS equations in the anomalous dispersive regime are then Hirota bilinearized, and exact bright solitons solutions are obtained. The analytical soliton solutions are also obtained. The results show that in both gain and loss cases the areas of the pulse envelopes remain preserved during the propagation in the fibers, demonstrating that bright solitary wave propagation is maintained in the cores. The results are discussed in detail.