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Differential-geometric structure and spectral properties of nonlinear completely integrable dynamical systems of the Mel'nikov type

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Ukrainian Mathematical Journal Aims and scope

Abstract

One considers V. K. Mel'nikov's new class of nonlinear dynamical systems, which is a generalization of the Korteweg-de Vries dynamical system. One investigates the differential-geometric and spectral properties of dynamical systems of Mel'nikov type, one gives their Hamiltonian form, one establishes the so-called gradient identity. The class of finite-zone potentials of a Sturm-Liouville operator, satisfying the given dynamical systems, is described.

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Authors and Affiliations

  1. Institute of Mathematics, Academy of Sciences of the Ukrainian SSR, Kiev

    V. G. Samoilenko

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  1. V. G. Samoilenko
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 5, pp. 655–659, May, 1990.

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Samoilenko, V.G. Differential-geometric structure and spectral properties of nonlinear completely integrable dynamical systems of the Mel'nikov type. Ukr Math J 42, 579–583 (1990). https://doi.org/10.1007/BF01065059

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  • DOI: https://doi.org/10.1007/BF01065059

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