Bifurcations in the Generalized Korteweg–de Vries Equation View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2018-02

AUTHORS

S. A. Kashchenko, M. M. Preobrazhenskaya

ABSTRACT

We study the generalized Korteweg–de Vries (KdV) equation and the Korteweg–de Vries–Burgers (KdVB) equation with periodic in the spatial variable boundary conditions. For various values of parameters, in a sufficiently small neighborhood of the zero equilibrium state we construct asymptotics of periodic solutions and invariant tori. Separately we consider the case when the stability spectrum of the zero solution contains a countable number of roots of the characteristic equation. In this case we state a special nonlinear boundary-value problem which plays the role of a normal form and determines the dynamics of the initial problem. More... »

PAGES

49-61

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Identifiers

URI

http://scigraph.springernature.com/pub.10.3103/s1066369x18020068

DOI

http://dx.doi.org/10.3103/s1066369x18020068

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1101521080


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