Optical soliton with damping and frequency chirping in fibre media

Nonlinear Schrödinger (NLS) equation which governs the propagation of single field in the fibre medium with pulse chirping and gain (loss) is considered. The integrability condition of NLS equation is arrived from the linear eigenvalue problem and is studied by using the Painlevé singularity structure analysis. From the Lax pair, soliton solution is constructed by using the Darboux–Bäcklund transformation technique. From the results, we show that the soliton is alive, i.e., pulse area is conserved with the inclusion of damping and pulse chirping effects.