Involutive distributions, invariant manifolds, and defining equations

Siberian Mathematical Journal

Volumn 43, Issue 3, 2002, Pages 428-438

  Kaptsov, O V ^a  

^a ENERGY SYSTEMS INSTITUTE   (Russian Federation)

Author keywords

Defining equation; Group analysis; Involutive distribution

Indexed keywords

EID: 0036261683     PISSN: 00374466     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1015403300242     Document Type: Article

References (23)

1. Ovsyannikov L. V., Group Analysis of Differential Equations [in Russian], Nauka, Moscow (1978).
2. Ibragimov N. Kh., Transformation Groups in Mathematical Physics [in Russian], Nauka, Moscow (1983).
3. Fushichych W. and Nikitin A., Symmetries of Maxwell's Equations, Reidel, Dordrecht (1987).
4. Andreev V. K., Kaptsov O. V., Pukhnachov V. V., and Rodionov A. A., Application of Group-Theoretic Methods to Hydrodynamics [in Russian], Nauka, Novosibirsk (1994).
5. Ovsyannikov L. V., "The SUBMODELS program. Gas dynamics," Prikl. Mar. Mekh., 58, No. 4, 30-55 (1994).
6. Bluman G. W. and Cole J. D., "The general similarity solution of the heat equation," J. Math. Mech., 18, 1025-1042 (1969).
7. Ames W. F., Nonlinear Partial Differential Equations in Engineering, Academic Press, New York (1972).
8. Kaptsov O. V., "Linear defining equations for differential constraints," Mat. Sb., 189, No. 12, 103-118 (1998).
9. Ëlkin V. I., Reduction of Nonlinear Control Systems. Differential Geometric Approach [in Russian], Nauka, Moscow (1997).
10. Smirnov V. I., A Course in Higher Mathematics. Vol. 4 [in Russian], Nauka, Moscow (1984).
11. Finikov S. P., Cartan's Method of Exterior Forms [in Russian], GIFML, Moscow (1948).
12. t = Δlogh," Prikl. Mekh. Tekhn. Fiz., 40, No. 1, 22-26 (1999).
13. Pukhnachov V. V., "Multidimensional exact solutions of a nonlinear diffusion equation," Prikl. Mekh. Tekhn. Fiz., 36, No. 2, 23-31 (1995).
14. Dorodnitsyn V. A., Knyazeva I. V., and Svirshchevskiǐ S. R., "Group properties of the heat equation with a source in two-dimensional and three-dimensional cases," Differentsial'nye Uravneniya, 19, No. 7, 1215-1223 (1983).
15. Galaktionov V. A., "Invariant subspaces and new explicit solutions to evolution equations with quadratic nonlinearities," Proc. Roy. Soc. Edinburgh Sect. A, 125A, No. 2, 225-246 (1995).
16. Rudykh G. A. and Semënov È. I., "Existence and construction of anisotropic solutions to the multidimensional equation of nonlinear diffusion. II," Sibirsk. Mat. Zh., 42, No. 1, 176-195 (2001).
17. Olver P. J., Applications of Lie Groups to Differential Equations [Russian translation], Mir, Moscow (1989).
18. Arrigo D. J., Broadbridge P., and Hill J. M., "Nonclassical symmetry solutions and the methods of Bluman-Cole and Clarkson Kruskal," J. Math. Phys., 34, No. 10, 4692-4703 (1993).
19. Olver P. J., "Direct reduction and differential constraints," Proc. Roy. Soc. London Sect. A, 444, 509-523 (1994).
20. Gibbons J. and Tsarev S. P., "Conformal maps and reductions of the Benney equations," Phys. Lett. A, 258, No. 4-6, 263-271 (1999).
21. Dodd R. K., Eilbeck J. C., Gibbon J. D., and Morris H. C., Solitons and Nonlinear Wave Equations [Russian translation], Mir, Moscow (1988).
22. Kim K. Y., Reid R. O., and Whitaker R. E., "On an open radiational boundary condition for weakly dispersive tsunami waves," J. Comput. Phys., 76, No. 2, 327-348 (1988).
23. Galaktionov V. A. and Posashkov S. A., "Examples of nonsymmetric extinction and blow-up for quasilinear heat equations," Differential Integral Equations, 8, No. 1, 87-103 (1995).