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On a class of quadratic conservation laws for Newton equations in Euclidean space

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Abstract

We discuss quadratic conservation laws for the Newton equations and the corresponding second-order Killing tensors in Euclidean space. In this case, the complete set of integrals of motion consists of polynomials of the second, fourth, sixth, and so on degrees in momenta, which can be constructed using the Lax matrix related to the hierarchy of the multicomponent nonlinear Schrödinger equation.

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Funding

The work is performed under the financial support of the Russian Science Foundation (grant No. 21-11-00141). The second author (E. O. Porubov) thanks the social investment program “Native cities” of the Public corporation “Gazprom Neft” for supporting the Chebyshev Laboratory of St. Petersburg State University.

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  1. St. Petersburg State University, St. Petersburg, Russia

    A. V. Tsiganov & E. O. Porubov

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  1. A. V. Tsiganov
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  2. E. O. Porubov
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Correspondence to A. V. Tsiganov.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2023, Vol. 216, pp. 350–382 https://doi.org/10.4213/tmf10447.

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Tsiganov, A.V., Porubov, E.O. On a class of quadratic conservation laws for Newton equations in Euclidean space. Theor Math Phys 216, 1209–1237 (2023). https://doi.org/10.1134/S0040577923080111

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  • DOI: https://doi.org/10.1134/S0040577923080111

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