论文信息 - Construction of Solutions for Nonintegrable Systems with the Help of the Painleve Test

Construction of Solutions for Nonintegrable Systems with the Help of the Painleve Test

The generalized Henon–Heiles system with an additional nonpolynomial term has been considered. In two nonintegrable cases with the help of the Painleve test new special solutions have been found as converging Laurent series, depending on three parameters. For some values of these parameters the obtained Laurent series coincide with the Laurent series of the known elliptic solutions. The calculations have been made with use of computer algebra system REDUCE. The obtained local solutions can assist to find the elliptic three parameters solutions. The corresponding algorithm has been realized in REDUCE and Maple.

S. Yu. Vernov | S. Vernov

[1] André Heck,et al. Introduction to Maple , 1993 .

[2] On two nonintegrable cases of the generalized Hénon-Heiles system , 2004, math-ph/0402049.

[3] M. Ablowitz,et al. A connection between nonlinear evolution equations and ordinary differential equations of P‐type. II , 1980 .

[4] André Heck,et al. Introduction to Maple, 3rd edition , 2003 .

[5] Sophie Kowalevski,et al. Sur le probleme de la rotation d'un corps solide autour d'un point fixe , 1889 .

[6] P. Painlevé. Leçons sur la théorie analytique des équations différentielles : professées à Stockholm(1895) , 1897 .

[7] R. Conte,et al. Analytic solitary waves of nonintegrable equations , 2003, nlin/0302051.

[8] Psi-Series Solutions of the Cubic Henon-Heiles System and Their Convergence , 1999, math/9904186.

[9] M. Hénon,et al. The applicability of the third integral of motion: Some numerical experiments , 1964 .

[10] C. Verhoeven,et al. Integration of a generalized Hénon-Heiles Hamiltonian , 2001, nlin/0112030.

[11] Constructing Solutions for the Generalized Hénon–Heiles System Through the Painlevé Test , 2002, math-ph/0209063.

[12] Sophie Kowalevski. Sur une propriété du système d'équations différentielles qui définit la rotation d'un corps solide autour d'un point fixe , 1890 .