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Multi-soliton solutions and a Bäcklund transformation for a generalized variable-coefficient higher-order nonlinear Schrödinger equation with symbolic computation |
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| Authors: | Xiang-Hua Meng Hong-Wu Zhu Bo Tian |
| Institution: | a School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China b Meteorology Center of Air Force Command Post, Changchun 130051, China c Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100083, China d Key Laboratory of Optical Communication and Lightwave Technologies, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China |
| Abstract: | In this paper, by virtue of symbolic computation, the investigation is made on a generalized variable-coefficient higher-order nonlinear Schrödinger 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 Bäcklund 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. |
| Keywords: | Symbolic computation Variable-coefficient higher-order nonlinear Schrö dinger equation Bilinear method Multi-soliton solutions Bä cklund transformation |
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