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Optical and Quantum Electronics

Erschienen in:

01.02.2018

The \(\left( \frac{\boldsymbol{G}^{\prime }}{\boldsymbol{G}},\frac{\boldsymbol{1}}{\boldsymbol{G}}\right)\)-expansion method and its applications for constructing many new exact solutions of the higher-order nonlinear Schrödinger equation and the quantum Zakharov–Kuznetsov equation

verfasst von: Elsayed M. E. Zayed, Ayad M. Shahoot, Khaled A. E. Alurrfi

Erschienen in: Optical and Quantum Electronics | Ausgabe 2/2018

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Abstract

In this article, we apply the two variable \(\left( \frac{G^{\prime }}{G}, \frac{1}{G}\right)\)-expansion method with the aid of symbolic computation to construct many new exact solutions for two higher-order nonlinear partial differential equatuions (PDEs) namely, the higher-order nonlinear Schrö dinger (NLS) equation with derivative non-kerr nonlinear terms describing pulse of the propagation beyond ultrashort range in optical communication systems and the higher-order nonlinear quantum Zakharov–Kuznetsov (QZK) equation which arises in quantum magneto plasma . Also, based on Liénard equation, we find many other diffrent new soliton solutions of the above NLS equation. Soliton solutions, periodic solutions, rational functions solutions and Jacobi elliptic functions solutions are obtained. Comparing our new solutions obtained in this article with the well-known solutions are given.

Vorheriger Artikel Scattering of Lommel beams by homogenous spherical particle in generalized Lorenz–Mie theory

Nächster Artikel Optical solitons in -dimensions under anti-cubic law of nonlinearity by analytical methods

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Titel: The -expansion method and its applications for constructing many new exact solutions of the higher-order nonlinear Schrödinger equation and the quantum Zakharov–Kuznetsov equation
verfasst von: Elsayed M. E. Zayed
Ayad M. Shahoot
Khaled A. E. Alurrfi
Publikationsdatum: 01.02.2018
Verlag: Springer US
Erschienen in: Optical and Quantum Electronics / Ausgabe 2/2018
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-018-1337-z

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