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Zayed, E. M. E.; Alurrfi, K. A. E.

Extended generalized \((Zakh\frac{G'}{G})\)-expansion method for solving the nonlinear quantum Zakharov-Kuznetsov equation. (English) Zbl 1355.35124

Ric. Mat. 65, No. 1, 235-254 (2016).
Summary: In this article, we apply the extended generalized \((\frac{G'}{G})\)-expansion method combined with the Jacobi elliptic equation to find new exact solutions of the nonlinear quantum Zakharov-Kuznetsov (QZK) equation with the aid of computer algebraic system Maple. Soliton solutions, periodic solutions, rational functions solutions and Jacobi elliptic functions solutions are obtained. Based on reductive perturbation technique and a series of transformation, the nonlinear QZK had been derived by many authors which can be reduced to a nonlinear ordinary differential equation (ODE) using the wave transformation. The extended generalized \((\frac{G'}{G})\)-expansion method is straightforward and concise, and it can also be applied to other nonlinear PDEs in mathematical physics.

Cited in 7 Documents

MSC:

35K99 Parabolic equations and parabolic systems
35C05 Solutions to PDEs in closed form
35Q40 PDEs in connection with quantum mechanics
35Q53 KdV equations (Korteweg-de Vries equations)
35B10 Periodic solutions to PDEs
35C08 Soliton solutions

Keywords:

extended generalized \((\frac{G'}{G})\)-expansion; Jacobi elliptic functions; exact solutions; nonlinear quantum Zakharov-Kuznetsov (QZK) equation; reductive perturbation technique; series of transformations

Software:

Maple
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Full Text: DOI

References:

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