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Intermediate asymptotics for solutions to the degenerate principal resonance equations

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Abstract

The system of two first-order differential equations that arises in averaging nonlinear systems over fast single-frequency oscillations is investigated. The averaging is performed in the neighborhood of the critical free frequency of a nonlinear system. In this case, the original equations differ from the principal resonance equations in the general case. The main result is the construction of the asymptotics of a two-parameter family of solutions in the neighborhood of a solution with unboundedly increasing amplitude. The results, in particular, provide a key to understanding the particle acceleration process in relativistic accelerators near the critical free frequency.

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Authors and Affiliations

  1. Institute of Mathematics and Computing Center, Russian Academy of Sciences, ul. Chernyshevskogo 112, Ufa, Bashkortostan, 450077, Russia

    L. A. Kalyakin

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  1. L. A. Kalyakin
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Original Russian Text © L.A. Kalyakin, 2006, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2006, Vol. 46, No. 1, pp. 83–94.

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Kalyakin, L.A. Intermediate asymptotics for solutions to the degenerate principal resonance equations. Comput. Math. and Math. Phys. 46, 79–89 (2006). https://doi.org/10.1134/S096554250601009X

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  • DOI: https://doi.org/10.1134/S096554250601009X

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