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Lax parametric integrability of nonlinear dynamical systems and the bifurcation problem for multisoliton separatrix manifolds

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Abstract

A new analytic approach to the description of the class of parametrically Lax-integrable nonlinear nonhomogeneous dynamical systems defined on functional manifolds that generalizes the well-known Mitropol'skii asymptotic method [1] is developed. Under a stipulated ɛ-deformation of the initial dynamical system, ɛ → 0, the bifurcation problem for multisoliton separatrix manifolds is studied on the basis of the concept of a generalized Mitropol'skii-Mel'nikov μ-function. In the special case of a nonlinear Korteweg -de Vries-Bürgers dynamical system, the structure of the bifurcation of a homoclinic separatrix trajectory is studied as a function of the embedding parameters of a soliton manifold in a functional space.

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Authors and Affiliations

  1. Institute of Applied Problems in Mechanics and Mathematics, Academy of Sciences of Ukraine, L'vov

    V. S. Kuibida & A. K. Prikarpatskii

Authors
  1. V. S. Kuibida
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  2. A. K. Prikarpatskii
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 3, pp. 365–379, March, 1992.

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Kuibida, V.S., Prikarpatskii, A.K. Lax parametric integrability of nonlinear dynamical systems and the bifurcation problem for multisoliton separatrix manifolds. Ukr Math J 44, 318–330 (1992). https://doi.org/10.1007/BF01063132

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  • DOI: https://doi.org/10.1007/BF01063132

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