Symmetry reduction of the boussinesq equation to ordinary differential equations

Reports on Mathematical Physics

Volumn 38, Issue 1, 1996, Pages 1-9

  Barannik, L F ^a   Lahno, H O ^b  

^a Pedagogical University   (Poland)

^b Pedagogical University   (Ukraine)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030210997     PISSN: 00344877     EISSN: None     Source Type: Journal    
DOI: 10.1016/0034-4877(96)87674-9     Document Type: Article

References (11)

1. [1] Boussinesq J.: Recherches théoriques sur l'écoulement des nappes d'eau infiltrées dans le sol et sur le débit des sources, J. Math. purs et appl. 10, No. 1 (1904), 5-78, (Complement 4, 363-394).
2. [1] Boussinesq J.: Recherches théoriques sur l'écoulement des nappes d'eau infiltrées dans le sol et sur le débit des sources, J. Math. purs et appl. 10, No. 1 (1904), 5-78, (Complement 4, 363-394).
3. [2] Sokolov J. D.: On some particular solutions of the Boussinesq equation, Ukrain. Math. Zh. 8 (1956), 54 (in Russian).
4. [3] Polubarynova-Kochina P. Y.: The Theory of the Flow of Ground Water, Nauka, Moscow 1977 (in Russian).
5. [4] Serova M. M.: in Algebraic-theoretical Method in Mathematical Physics Problems, Mathematical Institute, Kiev 1983, pp. 55-58 (in Russian).
6. [5] Fushchych W. I., Shtelen V. M. and Serov N. I.: Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics, Naukova Dumka, Kiev 1989 (in Russian; English version published by Kluwer, Dordrecht 1992).
7. [6] Ovsyannikov L. V.: Group Analysis of Differential Equations, Academic Press, New York 1982.
8. [7] Olver P.: Applications of Lie Groups to Differential Equations, Springer, New York 1987.
9. [8] Patera J., Winternitz P. and Zassenhaus H.: J. Math. Phys. 16 (1975), 1597.
10. [9] Fushchych W. I., Barannik L. F. and Barannik A. F.: Subgroup Analysis of Galilean, Poincaré Groups and Reduction of Nonlinear Equations, Naukova Dumka, Kiev 1991 (in Russian).
11. [10] Lang S.: Algebra, Addison-Wesley, Reading, Mass., New York 1965.