ACM Home Page
Please provide us with feedback. Feedback
Algorithmic determination of structure of infinite Lie pseudogroups of symmetries of PDEs
Full text PdfPdf (662 KB)
Source International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 1995 international symposium on Symbolic and algebraic computation table of contents
Montreal, Quebec, Canada
Pages: 1 - 6  
Year of Publication: 1995
ISBN:0-89791-699-9
Authors
I. G. Lisle  Mathematics Department, University of British Columbia, Vancouver B.C., Canada
G. J. Reid  Mathematics Department, University of British Columbia, Vancouver B.C., Canada
A. Boulton  Mathematics Department, University of British Columbia, Vancouver B.C., Canada
Sponsors
SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation
SIGNUM: ACM Special Interest Group on Numerical Mathematics
Publisher
ACM  New York, NY, USA
Bibliometrics
Downloads (6 Weeks): 2,   Downloads (12 Months): 13,   Citation Count: 0
Additional Information:

references   index terms   collaborative colleagues  

Tools and Actions: Request Permissions Request Permissions    Review this Article  
DOI Bookmark: Use this link to bookmark this Article: http://doi.acm.org/10.1145/220346.220347
What is a DOI?

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
1
G.W. Bluman and S. Kumei. 1989. Symmetries and Differential Equations. (Springer Verlag, New York).
 
2
I~.J. Caxtan 1904. Sur la structure des groupes infinis de transformations. Oeuvres Completes Part II, Vol. 2, 571-714. (Gauthier-Villars, Paris).
 
3
t~.j. Cartan. 1908. Les sous-groupes des groupes continus de transformations. Oeuvres Completes Part II, Vol. 2, 719-856. (Gauthier-Villars, Paris).
 
4
t~.J. Cartan. I937. Les probl@mes d'@quivalence. Oeuvres Compldtes Part II, Vol. 2, 1311-1334. (Gauthier- Villars, Paris).
 
5
l~.J. Cartan. 1937. La structure des groupes infihis. Oeuvres Comptgtes Part II, Vol. 2, 1335-1384. (Gauthier-Villars, Paris).
 
6
D. David, N. Kamran, D. Levi, and P. Winternitz. 1986. Symmetry reduction for the Kadomtsev-Petrviashvili equation using a loop algebra. Y. Math. Phys. 27: 1225- 1337.
 
7
R.B. Gardner. 1989. The Method of Equivalence and Its Applications. (SIAM, Philadelphia).
 
8
H. Goldschmidt. 1972, 73, 76. Sur la structure des @quations de Lie, I, II, III. J. Diff. Geom. 6: 357-373, 7': 67-95, 11: 167-223.
 
9
H. Goldschmidt and D.C. Spencer. 1976-78. On the nonlinear cohomology of Lie equations I, II. Acta Math. 136: 103-239, III, IV. J. Diff. Geom. 13: 409-526.
 
10
V. Guillemin. 1966. A Jordan-HSlder decomposition for certain classes of infinite-dimensional Lie algebras. J. Diff. Geom. 2: 313-345.
 
11
W. Hereman. 1994. Review of symbolic software for the computation of Lie symmetries of differential equations. Euromath Bull., 1: 45-79.
 
12
M. Hickman. 1993. The use of Maple in the search for symmetries. Research Report no. 77, Dept. of Mathematics (University of Canterbury, Christchurch, New Zealand).
 
13
M. Kuranishi. 1959. On the local theory of continuous infinite pseudo-groups. I. Nagoya Math. J. 15: 225- 260.
 
14
M. Kuranishi. 1961. On the local theory of continuous infinite pseudo-groups. II. Nagoya Math. J. 19: 55-91.
 
15
S. Lie. 1891. Foundations of the theory of infinite continuous transformation groups. (English translation in: R. Hermann. 1980. Cartanian Geometry, Nonlinear Waves and Solitons, Part B. (MathSci Press, Brookline, MA).
 
16
I.G. Lisle and G.J. Reid. 1994. Geometry and structure of Lie pseudogroups from infinitesimal defining systems. IAM Report 94-13, Univ. of British Columbia. Anonymous ftp to ftp. Jam. ubc. ca, file/techreports/ 1994/iam94-13. ps. gz.
 
17
B. Malgrange. 1972. t~quations de Lie, I, II. J. Diff. Geom. 6: 503-522), 7: 117-141.
 
18
E. Mansfield. 1994. A simple criterion for involutivity. Univ. of Exeter Preprint M94/16.
 
19
P.J. Olver. 1986. Application of Lie groups to differential equations. (Springer Verlag, New York).
 
20
L.V. Ovsiannikov. 1982. Group analysis of differential equations. (Academic Press, New York).
 
21
J.-F. Pommaret. 1978. Systems of Partial Differential Equations and Lie Pseudogroups (Gordon and Breach, New York).
 
22
G.J. Reid. 1991. Algorithms for reducing a system of PDEs to standard form, determining the dimension of its solution space and calculating its Taylor series solution. Euro. J. AppI. Maths. 2: 293-318.
 
23
G.J. Reid. 1991. Finding abstract Lie symmetry algebras of differential equations without integrating determining equations. Euro. J. AppI. Maths. 2: 319-340.
 
24
G.J. Reid, I.G. Lisle and A. Boulton. 1995. Characterising Lie equations by their infinitesimal symmetries. Preprint.
25
 
26
G.J. Reid, D.T. Weih, and A.D. Wittkopf. 1993. A point symmetry group of a differential equation which cannot be found using infinitesimal methods. In Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics. Eds.: N.H. Ibragimov, M. Torrisi and A. Valenti. 93-99. (Kluwer, Dordrecht).
 
27
G.J. Reid, A.D. Wittkopf and A. Boulton. 1994. Reduction of systems of nonlinear partial differential equations to simplified involutive forms. IAM Report 94-14, Univ. of British Columbia. Anonymous ftp to ftp. Jam. ubc. ca, file /techreports/1994/~am94-14. ps. gz.
 
28
G.J. Reid and A.D. Wittkopf. 1993. The long guide to the Standard Form package. Code and documentation by anonymous ftp to math.ubc, ca in directory /pub/reid/standardform.
29
 
30
I.M. Singer and S. Sternberg. 1965. The infinite groups of Lie and Cartan. I. The transitive groups. Y. d'Analyse Math. 15: 1-115.
 
31
E. Vessiot. 1904. Sur l'int@gration des syst~mes diff~rentiels qui admettent des groupes continus de transformations. Acta Math. 28: 307-349.

Collaborative Colleagues:
I. G. Lisle: colleagues
G. J. Reid: colleagues
A. Boulton: colleagues