Application of the group-theoretical method to physical problems

Preprint English OPEN
Abd-el-malek, Mina B.;
(1998)

The concept of the theory of continuous groups of transformations has attracted the attention of applied mathematicians and engineers to solve many physical problems in the engineering sciences. Three applications are presented in this paper. The first one is the proble... View more
  • References (17)
    17 references, page 1 of 2

    [2] Lie S., Math. Annalen, 1875, V.8, 220.

    [3] Abbott D.E. and Kline S.J., Simple Methods for Construction of Similarity Solutions of Partial Differential Equations. AFOSR TN 60-1163, Report MD-6, Dept. of Mech. Eng., Stanford University, 1960.

    [4] Taulbee D.R., Cozzarelli F.A. and Dym C.L., Similarity Solutions to some Nonlinear Impact Problems, Int. J. Nonlin. Mech., 1971, V.6.

    [5] Ames W.F. and Suliciu I., Some Exact Solutions for Wave Propagation in Viscelastic, Viscoplastic and Electrical Transmission Lines, Int. J. Nonlin. Mech., 1982, V.17, 223-230.

    [6] Sachdev P.L. and Philip V., Invariance Group Properties and Exact Solutions of Equations Describing Time-Dependent Free Surface Flows under Gravity, Q. Appl. Math., 1986, V.43, 463-480.

    [7] Richards P.C., Group Analysis of Equations Arising in Ocean Acoustics. Ph.D. dissertation, Georgia Institute of Technology, Atlanta, Georgia, USA, 1987.

    [8] Abd-el-Malek M.B., Boutros Y.Z. and Badran N.A., Group Method Analysis of Unsteady FreeConvective Boundary-Layer Flow on a Nonisothermal Vertical Flat Plate, J. Engg. Math., 1990, V.24, N. 4, 343-368.

    [9] Abd-el-Malek M.B. and Badran N.A., Group Method Analysis of Steady Free-Convective Laminar Boundary-Layer Flow on a Nonisothermal Vertical Circular Cylinder, J. Comput. Appl. Math., 1991, V.36, N. 2, 227-238.

    [10] Badran N.A. and Abd-el-Malek M.B., Group Method Analysis of the Dispersion of Gaseous Pollutants in the Presence of a Temperature Inversion. Proc. Modern group analysis: Advanced Analytical and Computational Methods in Mathematical Physics (Acireale, Catania, Italy 1992), 35-41, Kluwer Acad. Publ., Dordrecht, 1993.

    [11] Abd-el-Malek M.B., Group Method Analysis of Nonlinear Temperature Variation Across the Lake Depth. Proc. XXI International Colloquium on Group Theoretical Methods in Physics Group 21 (Goslar, Germany. 15-20 July, 1996), World Scientific, Singapore, 1997, 255-260.

  • Related Organizations (1)
  • Metrics
Share - Bookmark