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Darboux Transformation and Symbolic Computation on Multi-Soliton and Periodic Solutions for Multi-Component Nonlinear Schr¨odinger Equations in an Isotropic Medium

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Darboux Transformation and Symbolic Computation on Multi-Soliton and Periodic Solutions for Multi-Component Nonlinear Schr¨odinger Equations in an Isotropic Medium

Hai-Qiang Zhanga, Tao Xua, Juan Lia, Li-Li Lia, Cheng Zhanga, and Bo Tiana,b,c

aSchool of Science, Beijing Universityof Posts and Telecommunications, P. O. Box 122, Beijing 100876, China

bState KeyLaboratoryof Software Development Environment, Beijing Universityof Aeronautics and Astronautics, Beijing 100191, China

cKeyLaboratoryof Optical Communication and Lightwave Technologies, Ministryof Education, Beijing Universityof Posts and Telecommunications, Beijing 100876, China

Reprint requests to B. T.; E-mail: tian.bupt@yahoo.com.cn

Z. Naturforsch.64a,300 – 308 (2009); received June 17, 2008 / revised September 15, 2008 The Darboux transformation is applied to a multi-component nonlinear Schr¨odinger system, which governs the propagation of polarized optical waves in an isotropic medium. Based on the Lax pair associated with this integrable system, the formula for then-times iterative Darboux transforma- tion is constructed in the form of block matrices. The purelyalgebraic iterative algorithm is carried out via symbolic computation, and two different kinds of solutions of practical interest, i. e., bright multi-soliton solutions and periodic solutions, are also presented according to the zero and nonzero backgrounds.

Key words:Darboux Transformation; Soliton; Integrable System; Symbolic Computation.

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