Summary
The “s-parameter transformation group” and “infinitesimal transformation group” are applied to a set of plasma fluid equations to ascertain their self-similar behavior.
Similar content being viewed by others
References
H. C. S. Hsuan, K. E. Lonngren and W. F. Ames, Self-similar behavior of plasma fluid equations,J. Engineering Math., 8 (1974) 303–309.
W. F. Ames,Nonlinear Partial Differential Equations in Engineering, Academic Press, New York, Vol. I (1965) Ch. 4, Vol. II (1972) Ch. 2.
S. Lie,Differentialgleichungen, Chelsea Publishing Co., Bronx, New York (1967).
H. Shen and W. F. Ames, On invariant solutions of the Korteweg de Vries equation,Phys. Lett., 49 A (1974) 313–314.
H. Washimi and T. Taniuti, Propagation of ion-acoustic solitary waves of small amplitude,Phys. Rev. Lett., 17 (1966) 996–998.
M. Widner, I. Alexeff, W. D. Jones and K. E. Lonngren, Ion acoustic wave excitation and ion sheath evolution,Phys. Fluids, 13 (1970) 2532–2540.
A. J. A. Morgan, The reduction by one of the number of independent variables in some systems of partial differential equations,Quart. Journal Math., (Oxford) 3 (1952) 250–259.
Author information
Authors and Affiliations
Additional information
Supported in part by the National Science Foundation, Grant No. EN6-7400704.
Rights and permissions
About this article
Cite this article
Shen, H., Lonngren, K.E. Self-similar behavior of plasma fluid equations, part II. J Eng Math 10, 135–141 (1976). https://doi.org/10.1007/BF01535656
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01535656