A Truncated Painlevé Expansion and Exact Analytical Solutions for the Nonlinear Schrödinger Equation with Variable Coefficients

By using the truncated Painleve expansion analysis an auto-Backlund transformation is found for the nonlinear Schrödinger equation with varying dispersion, nonlinearity, and gain or absorption. Then, based on the obtained auto-Backlund transformation and symbolic computation, we explore some explicit exact solutions including soliton-like solutions, singular soliton-like solutions, which may be useful to explain the corresponding physical phenomena. Further, the formation and interaction of solitons are simulated by computer. - PACS Nos.: 05.45.Yv, 02.30.Jr, 42.65.Tg.