# Time-fractional Gardner equation for ion-acoustic waves in negative-ion-beam plasma with negative ions and nonthermal nonextensive electrons

## Abstract

Nonlinear propagation of ion-acoustic waves is investigated in a one-dimensional, unmagnetized plasma consisting of positive ions, negative ions, and nonthermal electrons featuring Tsallis distribution that is penetrated by a negative-ion-beam. The classical Gardner equation is derived to describe nonlinear behavior of ion-acoustic waves in the considered plasma system via reductive perturbation technique. We convert the classical Gardner equation into the time-fractional Gardner equation by Agrawal's method, where the time-fractional term is under the sense of Riesz fractional derivative. Employing variational iteration method, we construct solitary wave solutions of the time-fractional Gardner equation with initial condition which depends on the nonlinear and dispersion coefficients. The effect of the plasma parameters on the compressive and rarefactive ion-acoustic solitary waves is also discussed in detail.

- Authors:

- School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049 (China)
- School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000 (China)

- Publication Date:

- OSTI Identifier:
- 22410309

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 22; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; ANIONS; ELECTRONS; ION ACOUSTIC WAVES; ION BEAMS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; ONE-DIMENSIONAL CALCULATIONS; PERTURBATION THEORY; TIME DEPENDENCE; VARIATIONAL METHODS

### Citation Formats

```
Guo, Shimin, E-mail: gsm861@126.com, Mei, Liquan, E-mail: lqmei@mail.xjtu.edu.cn, and Zhang, Zhengqiang, E-mail: zhangzhengq@lzu.edu.cn.
```*Time-fractional Gardner equation for ion-acoustic waves in negative-ion-beam plasma with negative ions and nonthermal nonextensive electrons*. United States: N. p., 2015.
Web. doi:10.1063/1.4919264.

```
Guo, Shimin, E-mail: gsm861@126.com, Mei, Liquan, E-mail: lqmei@mail.xjtu.edu.cn, & Zhang, Zhengqiang, E-mail: zhangzhengq@lzu.edu.cn.
```*Time-fractional Gardner equation for ion-acoustic waves in negative-ion-beam plasma with negative ions and nonthermal nonextensive electrons*. United States. doi:10.1063/1.4919264.

```
Guo, Shimin, E-mail: gsm861@126.com, Mei, Liquan, E-mail: lqmei@mail.xjtu.edu.cn, and Zhang, Zhengqiang, E-mail: zhangzhengq@lzu.edu.cn. Fri .
"Time-fractional Gardner equation for ion-acoustic waves in negative-ion-beam plasma with negative ions and nonthermal nonextensive electrons". United States. doi:10.1063/1.4919264.
```

```
@article{osti_22410309,
```

title = {Time-fractional Gardner equation for ion-acoustic waves in negative-ion-beam plasma with negative ions and nonthermal nonextensive electrons},

author = {Guo, Shimin, E-mail: gsm861@126.com and Mei, Liquan, E-mail: lqmei@mail.xjtu.edu.cn and Zhang, Zhengqiang, E-mail: zhangzhengq@lzu.edu.cn},

abstractNote = {Nonlinear propagation of ion-acoustic waves is investigated in a one-dimensional, unmagnetized plasma consisting of positive ions, negative ions, and nonthermal electrons featuring Tsallis distribution that is penetrated by a negative-ion-beam. The classical Gardner equation is derived to describe nonlinear behavior of ion-acoustic waves in the considered plasma system via reductive perturbation technique. We convert the classical Gardner equation into the time-fractional Gardner equation by Agrawal's method, where the time-fractional term is under the sense of Riesz fractional derivative. Employing variational iteration method, we construct solitary wave solutions of the time-fractional Gardner equation with initial condition which depends on the nonlinear and dispersion coefficients. The effect of the plasma parameters on the compressive and rarefactive ion-acoustic solitary waves is also discussed in detail.},

doi = {10.1063/1.4919264},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 5,

volume = 22,

place = {United States},

year = {2015},

month = {5}

}