A simple criterion for involutivity

Journal of the London Mathematical Society

Volumn 54, Issue 2, 1996, Pages 323-345

  Mansfield, Elizabeth L ^a  

^a UNIVERSITY OF KENT   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000139515     PISSN: 00246107     EISSN: None     Source Type: Journal    
DOI: 10.1112/jlms/54.2.323     Document Type: Article

References (36)

1. R. L. BRYANT, S. S. CHERN, R. B. GARDNER, H. GOLDSCHMIDT and P. A. GRIFFITHS, Exterior differential systems, Mathematical Sciences Research Institute Publications 18 (Springer, New York, 1991).
2. B. BUCHBERGER, A survey on the method of Gröbner bases for solving problems in connection with systems of multi-variate polynomials, Symbolic and Algebraic Computation by Computer (eds. N. Inada and T. Soma; World Scientific, Singapore, 1985).
3. G. CARRÀ-FERRO, 'Gröbner bases and differential ideals', Proc. AAECC5, Menorca, Spain, Lecture Notes in Computer Science 356 (Springer, New York, 1989) 129-140.
4. H. CARTAN, Les systèmes differentiels extérieurs et leur applications géométriques (Hermann, Paris, 1945).
5. P. A. CLARKSON and E. L. MANSFIELD, 'Nonclassical symmetry reductions and exact solutions of nonlinear reaction-diffusion equations', Proc. NATOARW, 'Applications of Analytic and Geometric Methods to Nonlinear PDES', July, 1993, Exeter (ed. P. A. Clarkson; Kluwer, Dortrecht, 1994) 375-389.
6. P. A. CLARKSON and E. L. MANSFIELD, 'Symmetry reductions and exact solutions of a class of nonlinear heat equations', Phys. D 70 (1994) 250-288.
7. P. A. CLARKSON and E. L. MANSFIELD, 'Algorithms for the nonclassical method of symmetry reduction', SIAM J. Appl. Math. 54 (1994) 1693-1719.
8. D. Cox, J. LITTLE and D. O'SHEA, Ideals, varieties and algorithms (Springer, New York, 1992).
9. H. GOLDSCHMIDT, 'Integrability criteria for systems of partial differential equations', J. Differential Geom. 1 (1967) 269-307.
10. D. HARTLEY and R. TUCKER, 'A constructive implementation of the Cartan-Kähler theory of exterior differential systems', J. Symbolic Comput. 12 (1991) 655-667.
11. R. HARTSHORNE, Algebraic geometry (Springer, New York, 1977).
12. D. HILBERT, 'Über die Theorie der algebraischen Formen', Math. Ann. 36 (1890) 473-534.
13. P. J. HILTON and U. STAMMBACH, A course in homological algebra (Springer, New York, 1971).
14. A. HUSDON, 'Symbolic computation of involutivity of PDES', Masters Thesis, University of Sydney, 1987.
15. M. JANET, Leçons sur les systèmes d'équations (Gauthier-Villers, Paris, 1929).
16. E. R. KOLCHIN, Differential algebra and algebraic groups (Academic Press, New York, 1973).
17. R. MCGEHEE, 'Triple collisions in the collinear three-body problem', Invent. Math. 27 (1974) 191-227.
18. E. L. MANSFIELD, 'Differential Gröbner bases', Ph.D. Thesis, University of Sydney 1992.
19. E. L. MANSFIELD and E. D. FACKERELL, 'Differential Gröbner Bases', Macquarie University, preprint, 92/108.
20. F. OLLIVIER, 'Le problème de l'identifiabilité structurelle globale', Ph.D. Thesis, École Polytechnique 1990.
21. E. PANKRET'EV, 'Computations in differential and difference modules', Acta. Appl. Math. 16 (1989) 167-189.
22. J. F. POMMARET, Systems of partial differential equations and Lie pseudogroups (Gordon-Breach Science, New York, 1978).
23. J. F. POMMARET, Differential Galois theory (Gordon-Breach Science, New York, 1983).
24. J. F. POMMARET, Lie pseudogroups and mechanics (Gordon-Breach Science, New York, 1988).
25. G. REID, 'Algorithms for reducing a system of PDE to standard form, determining the dimension of its solution space and calculating its Taylor series solution', European J. Appl. Math 2 (1992) 293-318
26. J. F. RITT, Differential algebra, American Mathematical Society Colloquium Lectures 33 (1950) (Dover, New York, 1996).
27. C. RUIZ, 'Complexe de Koszul du symbole d'un système differential exterieur', C. R. Acad. Sci. Paris Série A-B 286 (1978) A55-A58.
28. F. SCHWARZ, 'An algorithm for deciding the size of symmetry groups', Computing 49 (1992) 95-115.
29. W. M. SEILER, P. J. VASSILIOU and C. ROGERS, 'Formal analysis of the Cauchy problem for a system associated with the (2+1)-dimensional Krichever-Novikov Equation', Acta Appl. Math. 42 (1996) 249-265.
30. D. SPENCER, 'Overdetermined systems of linear differential equations', Bull Amer. Math. Soc. 75 (1969) 179-239.
31. O. STORMARK, 'Formal and local solvability of PDEs', TRITA-MAT-1988-11, preprint.
32. V. TOPUNOV, 'Reducing systems of linear PDES to passive form', Acta Appl. Math. 16 (1989) 191-206.
33. P. VASSILIOU, 'Coupled systems of nonlinear wave equations and finite dimensional Lie algebras I', Acta. Appl. Math. 8 (1987) 107-147.
34. E. VESSIOT, 'Sur une théorie nouvelle des problèmes généraux d'integration', Bull. Soc. Math. France 52 (1924) 336-395.
35. R. WALKER, Algebraic curves (Springer, New York, 1978).
36. V. WEISPFENNING, 'Comprehensive Gröbner bases', J. Symbolic Comput. 14 (1992), 1-29.