Symbolic-computation construction of transformations for a more generalized nonlinear Schrödinger equation with applications in inhomogeneous
plasmas,optical fibers,viscous fluids and Bose-Einstein condensates |
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Authors: | Tao Xu Chun-Yi Zhang Guang-Mei Wei Juan Li Xiang-Hua Meng Bo Tian |
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Institution: | 1.School of Science, P.O. Box 49, Beijing University of Posts and Telecommunications,Beijing,China;2.Meteorology Center of Air Force Command Post,Changchun,China;3.Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics,Beijing,China;4.Department of Mathematics and LMIB,Beijing University of Aeronautics and Astronautics,Beijing,China |
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Abstract: | Currently, the variable-coefficient nonlinear Schr?dinger
(NLS)-typed models have attracted considerable attention in such
fields as plasma physics, nonlinear optics, arterial mechanics and
Bose-Einstein condensates. Motivated by the recent work of Tian et
al. Eur. Phys. J. B 47, 329 (2005)], this paper is devoted to
finding all the cases for a more generalized NLS equation with
time- and space-dependent coefficients to be mapped onto the
standard one. With the computerized symbolic computation, three
transformations and relevant constraint conditions on the
coefficient functions are obtained, which turn out to be more
general than those previously published in the literature. Via
these transformations, the Lax pairs are also derived under the
corresponding conditions. For physical applications, our
transformations provide the feasibility for more
currently-important inhomogeneous NLS models to be transformed
into the homogeneous one. Applications of those transformations to
several example models are illustrated and some soliton-like
solutions are also graphically discussed. |
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Keywords: | |
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