Invariance of the nonlinear generalized NLS equation under the Lie group of scaling transformations

The nonlinear generalized NLS equation in the sense of the Riemann–Liouville derivatives is considered. The symmetry properties of nonlinear generalized NLS equation is investigated by using the Lie group analysis method. By right of the obtained Lie point symmetries, it is shown that this equation...

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Bibliographic Details
Published in:Nonlinear dynamics 2015-12, Vol.82 (4), p.2001-2005
Main Authors: Zedan, Hassan A., Shapll, Seham, Abdel-Malek, Amira
Format: Article
Language:English
Subjects:
Automotive Engineering
Classical Mechanics
Control
Dynamical Systems
Engineering
Independent variables
Lie groups
Mechanical Engineering
Nonlinear differential equations
Ordinary differential equations
Original Paper
Vibration
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Summary:The nonlinear generalized NLS equation in the sense of the Riemann–Liouville derivatives is considered. The symmetry properties of nonlinear generalized NLS equation is investigated by using the Lie group analysis method. By right of the obtained Lie point symmetries, it is shown that this equation could transform into a nonlinear ordinary differential equation of fractional order with the new independent variable. The derivative is an Erdélyi–Kober derivative depending on a parameter α .
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-015-2294-8