1. Plasma Dynamics Group, School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Hicks Building, Sheffield S3 7RH, UK
2. Department of Mathematics, Jamoum University College, Umm Al-Qura University, Jamoum, 25375 Makkah, Saudi Arabia
3. Plasma Dynamics Group, Department of Automatic Control and Systems Engineering, The University of Sheffield, Mappin Street, Sheffield S1 3JD, UK