Conservation laws and Darboux transformation for the coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients in nonlinear optics

In this paper, by Darboux transformation and symbolic computation we investigate the coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients, which come from twin-core nonlinear optical fibers and waveguides, describing the effects of quintic nonlinearity on the ultrashort o...

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Bibliographic Details
Published in:Nonlinear dynamics 2014-09, Vol.77 (4), p.1331-1337
Main Authors: Qi, Feng-Hua, Ju, Hong-Mei, Meng, Xiang-Hua, Li, Juan
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Conservation laws
Control
Dynamical Systems
Energy conservation
Engineering
Mechanical Engineering
Nonlinear equations
Nonlinear optics
Nonlinearity
Optical fibers
Original Paper
Pulse propagation
Schrodinger equation
Solitary waves
Transformations
Vibration
Waveguides
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Summary:In this paper, by Darboux transformation and symbolic computation we investigate the coupled cubic–quintic nonlinear Schrödinger equations with variable coefficients, which come from twin-core nonlinear optical fibers and waveguides, describing the effects of quintic nonlinearity on the ultrashort optical pulse propagation in the non-Kerr media. Lax pair of the equations is obtained, and the corresponding Darboux transformation is constructed. One-soliton solutions are derived; some physical quantities such as the amplitude, velocity, width, initial phases, and energy are, respectively, analyzed; and finally an infinite number of conservation laws are also derived. These results might be of some value for the ultrashort optical pulse propagation in the non-Kerr media.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-014-1382-5