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Volume 9, Issue 2

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Learning about Differential Equations from Their Symmetries
Scott A. Herod

References

[1] S. Lie, "Über die Integration durch bestimmte Integrale von einer Klasser linearer partieller Differentualgleichungen," Arch, for Math., VI, Heft 3, 1881 S. 328-368.

[2] F. Schwartz, "Symmetries of Differential Equations: From Sophus Lie to Computer Algebra," Siam Review, 30, 1988 pp. 450-481.

[3] A. V. Bocharov, "Symbolic Solvers for Nonlinear Differential Equations," The Mathematica Journal, 3(2), 1993 pp. 63-69.

[4] G. W. Bluman and S. Kumei, Symmetries and Differential Equations, New York: Springer-Verlag, 1989.

[5] P. J. Olver, Applications of Lie Groups to Differential Equations, New York: Springer-Verlag, 1986.

[6] L. V. Ovsiannikov, Group Analysis of Differential Equations (W. F. Ames, ed.), New York: Academic Press, 1982.

[7] N. H. Ibragimov, Lie Group Analysis of Differential Equations, Boca Raton: CRC Press, 1994.

[8] G. Helzer, "Grobner Bases," The Mathematica Journal, 5(1), 1995 pp. 61-73.

[9] F. Schwartz, "An Algorithm for Determining the Size of Symmetry Groups," Computing, 49, 1992 pp. 95-115.

[10] S. A. Herod, "Families of Exact Solutions for the Barotropic Vorticity Equation," PAM Technical Report, 1995.

[11] M. J. Ablowitz and P. A. Clarkson, Solitons, Nonlinear Evolution Equations, and Inverse Scattering, Cambridge: Cambridge University Press, 1991.

[12] A. L. Rabenstein, Elementary Differential Equations with Linear Algebra, New York: Academic Press, 1975.

[13] G. W. Bluman and J. D. Cole, "The General Solution of the Heat Equation," Journal of Mathematical Mechanics, 18(11), 1969 pp. 1025-1042.

[14] P. A. Clarkson and M. D. Kruskal, "New Similarity Solutions of the Boussinesq Equation," Journal of Mathematical Physics, 30, 1989 pp. 2201-2213.



     
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