Symbolic computation on Bäcklund transformation and soliton solutions for a generalized nonlinear Schrödinger equation in inhomogeneous fibers

In this paper, we consider a generalized nonlinear Schrödinger equation with variable dispersion, electro-optic phase modulation and fiber gain/loss coefficients, which governs the propagation of solitons in an inhomogeneous fiber medium. By using the Hirota method and symbolic computation, one-, two- and N-soliton solutions and bilinear Bäcklund transformation are obtained. The condition assuring the solutions without singularities is given. The propagation of solitons is discussed analytically and graphically with respect to physical quantities such as amplitude, velocity and width. After the collisions, two solitons present three types: disappeared, together and separated. Collisions of three solitons are also derived. By asymptotic analysis, we found that the collision between the two solitons is elastic. (paper)