Applications of a simplified bilinear method to ion-acoustic solitary waves in plasma
In this paper, we propose a computational method for nonlinear partial differential equations modeling ion-acoustic waves as well as dusty plasmas in laboratory and space sciences. Many types of solitary waves including soliton solutions, N-soliton solutions and singular N-soliton solutions are derived. The characteristic line method and graphical analysis are applied to discuss the solitonic propagation and collision, including the bidirectional solitons and elastic interactions. Furthermore, the effects of inhomogeneities of media and nonuniformities of boundaries, depicted by the variable coefficients, on the soliton behavior are discussed.
- 12.W. Hereman, W. Zhuang, A MACSYMA program for the Hirota method, in 13th World Congress on Computation and Applied Mathematics (Criterion Press, Dublin, 1991), Vol. 2, p. 842Google Scholar
- 13.W. Hereman, W. Zhuang, Symbolic computation of solitons with Macsyma, in Computation and Applied Mathematics II: Differential Equations, edited by W.F. Ames, P.J. Van der Houwen (North Holland, Amsterdam, 1992), pp. 287–296Google Scholar
- 15.R. Hirota, The direct method in soliton theory (Cambridge University Press, Cambridge, 2004)Google Scholar