Symbolic computation on the Darboux transformation for a generalized variable-coefficient higher-order nonlinear Schrِdinger equation from fiber optics

Considering the propagation of ultrashort pulse in the realistic fiber optics, a generalized variable-coefficient higher-order nonlinear Schrödinger equation is investigated in this paper. Under certain constraints, a new 3 × 3 Lax pair for this equation is obtained through the Ablowitz–Kaup–Newell–Segur procedure. Furthermore, with symbolic computation, the Darboux transformation and nth-iterated potential transformation formula for such a model are explicitly derived. The corresponding features of ultrashort pulse in inhomogeneous optical fibers are graphically discussed by the one- and two-soliton-like solutions.