Eur. Phys. J. B 55, 323-332 (2007)
https://doi.org/10.1140/epjb/e2007-00058-x

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

¹ School of Science, P.O. Box 49, Beijing University of Posts and Telecommunications, Beijing, 100876, China
² Meteorology Center of Air Force Command Post, Changchun, 130051, China
³ Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, 100083, China
⁴ Department of Mathematics and LMIB, Beijing University of Aeronautics and Astronautics, Beijing, 100083, China

Corresponding author: ^a xutodd@ss.buaa.edu.cn

Received: 13 September 2006
Revised: 18 January 2007
Published online: 2 March 2007

Abstract

Currently, the variable-coefficient nonlinear Schrödinger (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.