# Exact solution of CKP equation and formation and interaction of two solitons in pair-ion-electron plasma

## Abstract

In the present investigation, cylindrical Kadomstev-Petviashvili (CKP) equation is derived in pair-ion-electron plasmas to study the propagation and interaction of two solitons. Using a novel gauge transformation, two soliton solutions of CKP equation are found analytically by using Hirota's method and to the best of our knowledge have been used in plasma physics for the first time. Interestingly, it is observed that unlike the planar Kadomstev-Petviashvili (KP) equation, the CKP equation admits horseshoe-like solitary structures. Another non-trivial feature of CKP solitary solution is that the interaction parameter gets modified by the plasma parameters contrary to the one obtained for Korteweg–de Vries equation. The importance of the present investigation to understand the formation and interaction of solitons in laboratory produced pair plasmas is also highlighted.

- Authors:

- Theoretical Plasma Physics Group, Department of Physics, Quaid-i-Azam University, Islamabad 45320 (Pakistan)
- (NCP), Quaid-i-Azam University Campus, Islamabad (Pakistan)
- National Center of Physics (NCP), Quaid-i-Azam University Campus, Islamabad (Pakistan)
- (Pakistan)

- Publication Date:

- OSTI Identifier:
- 22599911

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; CYLINDRICAL CONFIGURATION; ELECTRON PLASMA WAVES; EXACT SOLUTIONS; GAUGE INVARIANCE; INTERACTIONS; ION PLASMA WAVES; KORTEWEG-DE VRIES EQUATION; PLASMA

### Citation Formats

```
Batool, Nazia, Jahangir, R., National Center of Physics, Masood, W., COMSATS Institute of Information Technology, Islamabad, and Siddiq, M.
```*Exact solution of CKP equation and formation and interaction of two solitons in pair-ion-electron plasma*. United States: N. p., 2016.
Web. doi:10.1063/1.4960563.

```
Batool, Nazia, Jahangir, R., National Center of Physics, Masood, W., COMSATS Institute of Information Technology, Islamabad, & Siddiq, M.
```*Exact solution of CKP equation and formation and interaction of two solitons in pair-ion-electron plasma*. United States. doi:10.1063/1.4960563.

```
Batool, Nazia, Jahangir, R., National Center of Physics, Masood, W., COMSATS Institute of Information Technology, Islamabad, and Siddiq, M. Mon .
"Exact solution of CKP equation and formation and interaction of two solitons in pair-ion-electron plasma". United States.
doi:10.1063/1.4960563.
```

```
@article{osti_22599911,
```

title = {Exact solution of CKP equation and formation and interaction of two solitons in pair-ion-electron plasma},

author = {Batool, Nazia and Jahangir, R. and National Center of Physics and Masood, W. and COMSATS Institute of Information Technology, Islamabad and Siddiq, M.},

abstractNote = {In the present investigation, cylindrical Kadomstev-Petviashvili (CKP) equation is derived in pair-ion-electron plasmas to study the propagation and interaction of two solitons. Using a novel gauge transformation, two soliton solutions of CKP equation are found analytically by using Hirota's method and to the best of our knowledge have been used in plasma physics for the first time. Interestingly, it is observed that unlike the planar Kadomstev-Petviashvili (KP) equation, the CKP equation admits horseshoe-like solitary structures. Another non-trivial feature of CKP solitary solution is that the interaction parameter gets modified by the plasma parameters contrary to the one obtained for Korteweg–de Vries equation. The importance of the present investigation to understand the formation and interaction of solitons in laboratory produced pair plasmas is also highlighted.},

doi = {10.1063/1.4960563},

journal = {Physics of Plasmas},

number = 8,

volume = 23,

place = {United States},

year = {Mon Aug 15 00:00:00 EDT 2016},

month = {Mon Aug 15 00:00:00 EDT 2016}

}