The (3+1)-dimensional generalized mKdV-ZK equation for ion-acoustic waves in quantum plasmas as well as its non-resonant multiwave solution

doi:10.1088/1674-1056/abb3e2

Abstract The quantum hydrodynamic model for ion-acoustic waves in plasmas is studied. First, we design a new disturbance expansion to describe the ion fluid velocity and electric field potential. It should be emphasized that the piecewise function perturbation form is new with great difference from the previous perturbation. Then, based on the piecewise function perturbation, a (3+1)-dimensional generalized modified Korteweg-de Vries Zakharov-Kuznetsov (mKdV-ZK) equation is derived for the first time, which is an extended form of the classical mKdV equation and the ZK equation. The (3+1)-dimensional generalized time-space fractional mKdV-ZK equation is constructed using the semi-inverse method and the fractional variational principle. Obviously, it is more accurate to depict some complex plasma processes and phenomena. Further, the conservation laws of the generalized time-space fractional mKdV-ZK equation are discussed. Finally, using the multi-exponential function method, the non-resonant multiwave solutions are constructed, and the characteristics of ion-acoustic waves are well described.

Keywords: ion-acoustic waves piecewise function perturbation (3+1)-dimensional generalized time-space fractional mKdV-ZK equation non-resonant multiwave solution

Received: 18 May 2020
Revised: 29 July 2020
Accepted manuscript online: 01 September 2020

PACS:	45.10.Hj	(Perturbation and fractional calculus methods)
	11.30.-j	(Symmetry and conservation laws)
	02.30.Jr	(Partial differential equations)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11975143), the Natural Science Foundation of Shandong Province of China (Grant No. ZR2018MA017), the Taishan Scholars Program of Shandong Province, China (Grant No. ts20190936), and the Shandong University of Science and Technology Research Fund (Grant No. 2015TDJH102).

Corresponding Authors: ^†Corresponding author. E-mail: hwyang1979@163.com

Cite this article:

Xiang-Wen Cheng(程香雯), Zong-Guo Zhang(张宗国), and Hong-Wei Yang(杨红卫) The (3+1)-dimensional generalized mKdV-ZK equation for ion-acoustic waves in quantum plasmas as well as its non-resonant multiwave solution 2020 Chin. Phys. B 29 124501

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The (3+1)-dimensional generalized mKdV-ZK equation for ion-acoustic waves in quantum plasmas as well as its non-resonant multiwave solution

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