Xue, Yu-Shan; Tian, Bo; Zhang, Hai-Qiang; Liu, Wen-Jun; Li, Li-Li; Qi, Feng-Hua; Zhan, Yan Darboux transformation and soliton solutions for inhomogeneous coupled nonlinear Schrödinger equations with symbolic computation. (English) Zbl 1186.35213 Commun. Theor. Phys. 52, No. 5, 888-896 (2009). Summary: With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrödinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have potential applications in the long-distance communication of two-pulse propagation in inhomogeneous optical fibers. Based on the obtained nonisospectral linear eigenvalue problems (i.e., Lax pair), we construct the Darboux transformation for such a model to derive the optical soliton solutions. In addition, through the one- and two-soliton-like solutions, we graphically discuss the features of picosecond solitons in inhomogeneous optical fibers. MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 35Q51 Soliton equations 35C08 Soliton solutions 35A30 Geometric theory, characteristics, transformations in context of PDEs 37K35 Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems 78A10 Physical optics Keywords:variable-coefficient coupled nonlinear Schrödinger equations; optical solitons; Darboux transformation; symbolic computation PDFBibTeX XMLCite \textit{Y.-S. Xue} et al., Commun. Theor. Phys. 52, No. 5, 888--896 (2009; Zbl 1186.35213) Full Text: DOI