Constructing solutions for the generalized hénon-heiles system through the painlevé test

Theoretical and Mathematical Physics

Volumn 135, Issue 3, 2003, Pages 792-801

  Vernov, S Yu ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Elliptic functions; H non Heiles system; Laurent series; Nonintegrable systems; Painlev test; Polynomial potential; Singularity analysis

Indexed keywords

EID: 0037865558     PISSN: 00405779     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1024074702960     Document Type: Article

References (51)

1. S. Kowalevski, Acta. Math., 12, 177 (1889); 14, 81 (1890).
2. S. Kowalevski, Acta. Math., 12, 177 (1889); 14, 81 (1890).
3. V. V. Golubev, Lecture Notes on Integrating Equations of Motion of a Massive Solid Body Near Fixed Point [in Russian], Gostekhizdat, Moscow (1953); Reprinted by Regul. Chaotic Dyn., Moscow (2002).
4. V. V. Golubev, Lecture Notes on Integrating Equations of Motion of a Massive Solid Body Near Fixed Point [in Russian], Gostekhizdat, Moscow (1953); Reprinted by Regul. Chaotic Dyn., Moscow (2002).
5. A. Goriely, Regul. Chaotic Dyn., 5, 1 (2000).
6. V. V. Golubev, Lecture Notes on the Analytical Theory of Differential Equations [in Russian], Gostekhizdat, Moscow (1950).
7. E. Hille, Ordinary Differential Equations in the Complex Domain, Wiley, New York (1976).
8. P. Painlevé, Leçons sur la théorie analytique des Équations Différentelles (Leçons de Stockholm, 1895), Hermann, Paris (1896); Reprinted in:, Oeuvres de P. Painlevé, Vol. 1, Editions du CNRS, Paris (1973); Bull Soc. Math. France, 28, 201 (1900); Acta Math., 25, 1 (1902).
9. P. Painlevé, Leçons sur la théorie analytique des Équations Différentelles (Leçons de Stockholm, 1895), Hermann, Paris (1896); Reprinted in:, Oeuvres de P. Painlevé, Vol. 1, Editions du CNRS, Paris (1973); Bull Soc. Math. France, 28, 201 (1900); Acta Math., 25, 1 (1902).
10. P. Painlevé, Leçons sur la théorie analytique des Équations Différentelles (Leçons de Stockholm, 1895), Hermann, Paris (1896); Reprinted in:, Oeuvres de P. Painlevé, Vol. 1, Editions du CNRS, Paris (1973); Bull Soc. Math. France, 28, 201 (1900); Acta Math., 25, 1 (1902).
11. P. Painlevé, Leçons sur la théorie analytique des Équations Différentelles (Leçons de Stockholm, 1895), Hermann, Paris (1896); Reprinted in:, Oeuvres de P. Painlevé, Vol. 1, Editions du CNRS, Paris (1973); Bull Soc. Math. France, 28, 201 (1900); Acta Math., 25, 1 (1902).
12. T. Bountis, H. Segur, and F. Vivaldi, Phys. Rev. A, 25, 1257 (1982).
13. A. Ramani, B. Grammaticos, and T. Bountis, Phys. Rep., 180, 159 (1989).
14. M. Tabor, Chaos and Integrability in Nonlinear Dynamics: An Introduction, Wiley, New York (1989).
15. N. Ercolani and E. D. Siggia, Phys. Lett. A, 119, 112 (1986); Phys. D, 34, 303 (1989).
16. N. Ercolani and E. D. Siggia, Phys. Lett. A, 119, 112 (1986); Phys. D, 34, 303 (1989).
17. H. Yoshida, Celest. Mech., 31, 363, 381 (1983).
18. H. Yoshida, Phys. D, 128, 53 (1999).
19. V. V. Kozlov, Symmetry, Topology, and Resonances in Hamiltonian Mechanics [in Russian], Udmurtia State University, Izhevsk (1995); English transl., Springer, Berlin (1995).
20. M. J. Ablowitz, A. Ramani, and H. Segur, Lett. Nuovo Cimento, 23, 333 (1978); J. Math. Phys., 21, 715, 1006 (1980).
21. M. J. Ablowitz, A. Ramani, and H. Segur, Lett. Nuovo Cimento, 23, 333 (1978); J. Math. Phys., 21, 715, 1006 (1980).
22. J. Weiss, M. Tabor, and G. Carnevale, J. Math. Phys., 24, 522 (1983).
23. J. Weiss, J. Math. Phys., 24, 1405 (1983).
24. A. C. Newell, M. Tabor, and Y. B. Zeng, Phys. D, 29, 1 (1987).
25. R. Conte, A. P. Fordy, and A. Pickering, Phys. D, 69, 33 (1993).
26. R. Conte, ed., The Painlevé Property: One Century Later (CRM Ser. Math. Phys.), Springer, Berlin (1999).
27. R. Conte, "Exact solutions of nonlinear partial differential equations by singularity analysis," nlin.SI/0009024 (2000).
28. J. Weiss, Phys. Lett. A, 102, 329 (1984); 105, 387 (1984).
29. J. Weiss, Phys. Lett. A, 102, 329 (1984); 105, 387 (1984).
30. R. Sahadevan, Theor. Math. Phys., 99, 776 (1994).
31. J. Springael, R. Conte, and M. Musette, Regul. Chaotic Dyn., 3, No. 1, 3 (1998); solv-int/9804008 (1998).
32. G. Contopoulos, Z. Astrophys., 49, 273 (1960); Astron. J., 68, 1 (1963).
33. G. Contopoulos, Z. Astrophys., 49, 273 (1960); Astron. J., 68, 1 (1963).
34. M. Hénon and C. Heiles, Astron. J., 69, 73 (1964).
35. Y. F. Chang, M. Tabor, J. Weiss, and G. Corliss, Phys. Lett. A, 85, 211 (1981).
36. Y. F. Chang, M. Tabor, and J. Weiss, J. Math. Phys., 23, 531 (1982).
37. S. Yu. Vernov, "The Painlevé analysis and special solutions for nonintegrable systems," math-ph/0203003 (2002).
38. D. L. Rod, J. Differential Equations, 14, 129 (1973).
39. J. Podolský and K. Veselý, Phys. Rev. D, 58, 081501 (1998).
40. F. Kokubun, Phys. Rev. D, 57, 2610 (1998).
41. Y. Guo and C. Grotta Ragazza, Comm. Pure Appl. Math., 49, 1145 (1996).
42. G. Tondo, Theor. Math. Phys., 99, 796 (1994).
43. F. Kokubun, Phys. Lett. A, 245, 358 (1998).
44. R. Conte, M. Musette, and C. Verhoeven, J. Math. Phys., 43, 1906 (2002); nlin.SI/0112030 (2001).
45. A. Erdélyi et al., eds., Higher Transcendental Functions (Based on notes left by H. Bateman), Vol. 3, MCGraw-Hill, New York (1955).
46. E. I. Timoshkova, Astron. Rep., 43, 406 (1999).
47. A. C. Hearn, REDUCE User's Manual Vers. 3.6, RAND Publ., Santa Monica, Calif. (1995); http://www.unikoeln.de/REDUCE/3.6/doc/reduce/.
48. V. F. Edneral, A. P. Kryukov, and A. Ya. Rodionov, REDUCE: Programming Language for Analytical Calculations [in Russian], Moscow State University, Moscow (1989).
49. V. A. Murav'ev and D. E. Burlankov, MATHEMATICA [in Russian], Regul. Chaotic Dyn., Moscow (2000).
50. S. Melkonian, J. Nonlinear Math. Phys., 6, 139 (1999); math.DS/9904186 (1999).
51. S. Melkonian and A. Zypchen, Nonlinearity, 8, 1143 (1995).