Study of Ion-Acoustic Solitary Waves in a Magnetized Plasma Using the Three-Dimensional Time-Space Fractional Schamel-KdV Equation

• Published in: Complexity (New York, N.Y.) Vol. 2018; no. 2018; pp. 1 - 17
• Main Authors: Liu, Jianxin, Zhang, Yong, Fu, Chen, Guo, Min, Yang, Hongwei
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01.01.2018; Hindawi; John Wiley & Sons, Inc; Wiley
• Subjects: Acoustic properties; Acoustics; Applied mathematics; Calculus; Conservation laws; Fractional calculus; Inverse method; Korteweg-Devries equation; Mathematical models; Methods; Multiscale analysis; Partial differential equations; Perturbation methods; Physics; Plasma; R&D; Relativism; Research & development; Researchers; Solitary waves; Symmetry; Three dimensional models
• ISSN: 1076-2787; 1099-0526
• DOI: 10.1155/2018/6852548

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.