Abstract
For a special choice of the three interparticle coupling constants in the three-body version of a many-body problem in the plane that was recently investigated, the general solution of the equations of motion can be written in closed form (and is remarkably simple). We also discuss another analogous three-body problem and obtain two third-order highly nonlinear autonomous ODEs whose general solutions, we conjecture, are entire. In other words, we conjecture that these ODEs feature (a strong version of) the Painlevé property.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
F. Calogero and J.-P. Françoise, Inverse Problems, 17, 1–8 (2001).
F. Calogero, Classical Many-Body Problems Amenable to Exact Treatments (Lect. Notes Phys., Vol. M. 66), Springer, Berlin (2001).
F. Calogero, J.-P. Françoise, and M. Sommacal, “Periodic solutions of a many-rotator problem in the plane: II. Analysis of various motions,” J. Nonlinear Math. Phys. (in press).
F. Calogero, Nuovo Cimento B, 43, 177–241 (1978); Phys. D, 152–153, 78–84 (2001).
F. Calogero, J. Math. Phys., 39, 5268–5291 (1998).
F. Calogero, J. Math. Phys., 38, 5711–5719 (1997).
F. Calogero, “Solution of a three-body problem in the plane,” Phys. Lett. A (submitted).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Calogero, F. Solvable Three-Body Problem and Painlevé Conjectures. Theoretical and Mathematical Physics 133, 1445–1454 (2002). https://doi.org/10.1023/A:1021182307514
Issue Date:
DOI: https://doi.org/10.1023/A:1021182307514