Analytic dark soliton solutions for a generalized variable-coefficient higher-order nonlinear Schrödinger equation in optical fibers using symbolic computation

In this paper, a generalized variable-coefficient nonlinear Schrödinger equation with higher-order and gain/loss effects which can be used to describe the femtosecond pulse propagation is analytically investigated via symbolic computation. Under sets of coefficient constraints, such an equation is transformed into a completely integrable constant-coefficient higher-order nonlinear Schrödinger equation. Furthermore, through the transformation, the dark one- and two-soliton solutions for the generalized variable-coefficient higher-order nonlinear Schrödinger equation are derived by means of the bilinear method.