Parametric integration by Laks of nonlinear dynamic systems and problem of splitting of multisoliton separatrix varieties
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 $\varepsilon$-deformation...
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| Date: | 1992 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8104 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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 $\varepsilon$-deformation of the initial dynamical system, $\varepsilon\rightarrow0$, the bifurcation problem for multisoliton separatrix manifolds is studied on the basis of the concept of a generalized Mitropol'skii-Mel'nikov $\mu$-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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