Multi-soliton solutions and a Backlund transformation for a generalized variable-coefficient higher-order nonlinear Schrodinger equation with symbolic computation

In this paper, by virtue of symbolic computation, the investigation is made on a generalized variable-coefficient higher-order nonlinear Schrodinger equation with varying higher-order effects and gain or loss, which can describe the femtosecond optical pulse propagation in a monomode dielectric waveguide. A modified dependent variable transformation is introduced into the bilinear method to transform such an equation into a variable-coefficient bilinear form. Based on the formal parameter expansion technique, the multi-soliton solutions of this equation are obtained through the bilinear form under sets of parametric constraints. A Backlund transformation in bilinear form is also obtained for the first time in this paper. Finally, discussions on the analytic soliton solutions are given and various propagation situations are illustrated. (c) 2007 Elsevier B.V. All rights reserved.