With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrodinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have pot...With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrodinger 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.展开更多
Based on the generalized dressing method, we propose integrable variable coefficient coupled cylin-drical nonlinear SchrSdinger equations and their Lax pairs. As applications, their explicit solutions and their reduct...Based on the generalized dressing method, we propose integrable variable coefficient coupled cylin-drical nonlinear SchrSdinger equations and their Lax pairs. As applications, their explicit solutions and their reductions are constructed.展开更多
An extension of the Lie algebra A_~n-1 has been proposed [Phys. Lett. A, 2003, [STHZ]310:19-24]. In this paper, the new Lie algebra was used to construct a new higher dimensional loop algebra [AKG～]. Based on the loo...An extension of the Lie algebra A_~n-1 has been proposed [Phys. Lett. A, 2003, [STHZ]310:19-24]. In this paper, the new Lie algebra was used to construct a new higher dimensional loop algebra [AKG～]. Based on the loop algebra [AKG～], the integrable couplings system of the NLS-MKdV equations hierarchy was obtained. As its reduction case, generalized nonlinear NLS-MKdV equations were obtained. The method proposed in this letter can be applied to other hierarchies of evolution equations.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.60772023 the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.BUAA-SKLSDE-09KF-04+2 种基金Beijing University of Aeronautics and Astronautics,by the National Basic Research Program of China (973 Program) under Grant No.2005CB321901the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos.20060006024 and 200800130006Chinese Ministry of Education
文摘With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrodinger 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.
基金Supported by a grant from City University of Hong Kong(Project No:7002366)the support by National Natural Science Foundation of China(Project No:11301149)+1 种基金Henan Natural Science Foundation For Basic Research under Grant No:132300410310Doctor Foundation of Henan Institute of Engeering under Grant No:D2010007
文摘Based on the generalized dressing method, we propose integrable variable coefficient coupled cylin-drical nonlinear SchrSdinger equations and their Lax pairs. As applications, their explicit solutions and their reductions are constructed.
文摘An extension of the Lie algebra A_~n-1 has been proposed [Phys. Lett. A, 2003, [STHZ]310:19-24]. In this paper, the new Lie algebra was used to construct a new higher dimensional loop algebra [AKG～]. Based on the loop algebra [AKG～], the integrable couplings system of the NLS-MKdV equations hierarchy was obtained. As its reduction case, generalized nonlinear NLS-MKdV equations were obtained. The method proposed in this letter can be applied to other hierarchies of evolution equations.
