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Z. Naturforsch. 66a, 552 – 558
(2011)
doi:10.5560/ZNA.2011-0017
Reductions and Solutions of Two Types of Coupled Nonlinear Evolution Equations in Optical Fibers and Fluid Dynamics
1 School of Science, P. O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China
2 State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
3 Key Laboratory of Information Photonics and Optical Communications (BUPT),
Ministry of Education, P. O. Box 128, Beijing University of Posts and Telecommunications,
Beijing 100876, China
Received December 18, 2010 / revised May 6, 2011
Reprint requests to: B. T.; E-mail:
tian.bupt@yahoo.com.cn
Under investigation in this paper are the coupled nonlinear Schrödinger equations (CNLSEs) and coupled Burgers-type equations (CBEs), which are, respectively, a model for certain birefringent optical fibers Raman-scattering, Kerr and gain/loss effects, and a generalized model in fluid dynamics. Special attention should be paid to the existing claim that the solitons for the CNLSEs do not exist. Through certain dependent-variable transformations, the CNLSEs are reduced to a Manakov system and the CBEs are linearized. In that way, some new solutions of the CNLSEs and CBEs are obtained via symbolic computation. Especially the one-dark-soliton-like solutions for the CNLSEs have been found, against the existing claim.
Key words: Coupled Nonlinear Schrödinger Equations; Coupled Burgers-Type Equations; Dependent-Variable Transformation; Symbolic Computation; Soliton.
PACS numbers: 02.30.Ik; 02.30.Jr; 04.20.Jb; 05.45.Yv; 02.70.Wz