Exact solutions of cylindrical and spherical dust ion acoustic waves
- 1 October 2003
- journal article
- letter
- Published by AIP Publishing in Physics of Plasmas
- Vol. 10 (10) , 4162-4165
- https://doi.org/10.1063/1.1605741
Abstract
Cylindrical and spherical modified Korteweg–de Vries (KdV) equations are derived for dust ion acoustic waves. It is shown that a suitable coordinate transformation reduces the cylindrical KdV equation into the ordinary KdV equation which can be solved analytically. A completely different analytical solution is obtained using the group analysis method. However, for cylindrical and spherical modified KdV equations group analysis method yields trivial analytical solutions. Numerically, solutions to these modified KdV equations are obtained assuming initial profiles similar to those in one-dimensional soliton solutions.Keywords
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