The Inverse Problem of the Birkhoff-Gustavson Normalization of the Perturbed Harmonic Oscillators with Cubic Potentials

Article type: Research Article

Authors: Uwano, Yoshio^{a; 1} | Gusev, Alexander^{b; 2} | Rostovtsev, Vitaly^{c; 3} | Vinitsky, Sergue I.^{d; 4; 5}

Affiliations: [a] Department of Applied Mathematics and Physics, Kyoto University, Kyoto 606-8501, Japan | [b] Science Center of Applied Investigations, Joint Institute for Nuclear Research, Dubna 141980 Moscow Region, Russia | [c] Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna 141980 Moscow Region, Russia | [d] Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, Dubna 141980, Moscow Region, Russia

Correspondence: [5] The address for manuscript correspondence: Sergue I. Vinitsky, BLTP, JINR, Dubna, Moscow region, 141980, Russia. E-mail: [email protected]. Fax: +7 09621 65084. Phone: +7 09621 63348.

Note: [1] Supported by Grant-in-Aid Exploratory Research No.11875022 from JSPS..

Note: [2] Supported by Grant Nos.00-02-16337, 00-01-00617 and 00-02-81023-Bel2000a from RFBR.

Note: [3] Supported by Grant Nos.00-02-16337, 00-01-00617 and 00-02-81023-Bel2000a from RFBR.

Note: [4] Supported by Grant Nos.00-02-16337, 00-01-00617 and 00-02-81023-Bel2000a from RFBR.

Abstract: A new variant of the symbolic computing program ANFER reproduces the deep relation between the Bertrand-Darboux integrability condition (BDIC) for the perturbed harmonic oscillators with homogeneous cubic polynomial potentials (PHOCPs) and with quartic potentials (PHOQPs) which was discovered in the inverse problem for PHOCPs [1].

Keywords: Normal form, computer algebra, integrability

DOI: 10.3233/JCM-2002-21-237

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 2, no. 1-2, pp. 271-275, 2002