Study of ion-acoustic solitary waves in a magnetized plasma using the three-dimensional time-space fractional Schamel-KdV equation
type: Item
instance of: scholarly article
title: Study of ion-acoustic solitary waves in a magnetized plasma using the three-dimensional time-space fractional Schamel-KdV equation
zbMATH Open document ID: 1398.35196
DOI: 10.1155/2018/6852548
author: Min Guo
author: Chen Fu
author: Yong Zhang
author: Jianxin Liu
author: Hong-Wei Yang
published in: Complexity
publication date: 2018-09-27T00:00:00Z
review text: Summary: The study of ion-acoustic solitary waves in a magnetized plasma has long been considered to be an important research subject and plays an increasingly important role in scientific research. Previous studies have focused on the integer-order models of ion-acoustic solitary waves. With the development of theory and advancement of scientific research, fractional calculus has begun to be considered as a method for the study of physical systems. The study of fractional calculus has opened a new window for understanding the features of ion-acoustic solitary waves and can be a potentially valuable approach for investigations of magnetized plasma. In this paper, based on the basic system of equations for ion-acoustic solitary waves and using multi-scale analysis and the perturbation method, we have obtained a new model called the three-dimensional(3D) Schamel-KdV equation. Then, the integer-order 3D Schamel-KdV equation is transformed into the time-space fractional Schamel-KdV (TSF-Schamel-KdV) equation by using the semi-inverse method and the fractional variational principle. To study the properties of ion-acoustic solitary waves, we discuss the conservation laws of the new time-space fractional equation by applying Lie symmetry analysis and the Riemann-Liouville fractional derivative. Furthermore, the multi-soliton solutions of the 3D TSF-Schamel-KdV equation are derived using the Hirota bilinear method. Finally, with the help of the multi-soliton solutions, we explore the characteristics of motion of ion-acoustic solitary waves.
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 6944915
zbMATH Keywords: ion-acoustic solitary waves
zbMATH Keywords: magnetized plasma
zbMATH Keywords: three-dimensional time-space fractional Schamel-KdV equation
zbMATH Keywords: semi-inverse method
zbMATH Keywords: fractional variational principle
zbMATH Keywords: conservation laws
zbMATH Keywords: Lie symmetry analysis
zbMATH Keywords: Riemann-Liouville fractional derivative
zbMATH Keywords: Hirota bilinear method
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/6852548
OpenAlex ID: W2810494400
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description: scientific article; zbMATH DE number 6944915