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Elliptic solutions of equations of motion of the interacting particles in an external field |
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| Affiliation: | 1. Department of Mathematics, UCLA, Los Angeles, CA 90095, United States;2. Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19103, United States;3. Universidad Nacional Autónoma de México, Centro de Ciencias Matemáticas, Apartado Postal 61-3 Xangari, 58089 Morelia, Mich., Mexico;1. Dipartimento di Matematica e Informatica “U. Dini”, University of Firenze, Firenze, Italy;2. Science Institute, University of Iceland, Iceland |
| Abstract: | We consider the problem of finding analytic solutions to the equations of motion of completely integrable systems of two interacting particles on a straight line in an external field of an anharmonic oscillator. It is shown that for all values of the parameters of the interaction hamiltonian there exist solutions dependent on time through the jacobian elliptic functions. |
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