Geodesic
Bifurcations in the generalized Korteweg--de Vries equation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2018), pp. 54-68

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We consider the generalized Korteweg–de Vries (KdV) equation and the Korteweg–de Vries–Burgers (KdVB) equation with boundary condition by space variable. For different values of the parameters in a sufficiently small neighborhood of the zero equilibrium state we construct the asymptotic behavior of periodic solutions and invariant tori. Separately we consider the case of the characteristic equation has a countable number of roots in the range of stability of the zero solution. In this situation we build a special nonlinear boundary-value problem, which plays the role of a normal form and determines the dynamics of the original problem.
Keywords: partial derivative differential equation, normal form method
Mots-clés : torus, bifurcation. 
@article{IVM_2018_2_a5,
     author = {S. A. Kashchenko and M. M. Preobrazhenskaya},
     title = {Bifurcations in the generalized {Korteweg--de} {Vries} equation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {54--68},
     publisher = {mathdoc},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_2_a5/}
}
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S. A. Kashchenko; M. M. Preobrazhenskaya. Bifurcations in the generalized Korteweg--de Vries equation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2018), pp. 54-68. http://geodesic.mathdoc.fr/item/IVM_2018_2_a5/