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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 4, Pages 693–712 (Mi zvmmf159)  

This article is cited in 3 scientific papers (total in 3 papers)

Fronts, traveling fronts, and their stability in the generalized Swift–Hohenberg equation

N. E. Kulagina, L. M. Lermanb, T. G. Shmakovac

a State University of Management, Ryazanskii pr. 99, Moscow, 109542, Russia
b Research Institute for Applied Mathematics and Cybernetics, Nizhni Novgorod State University, ul. Ul'yanova 10, Nizhni Novgorod, 603005, Russia
c MATI Russian State University of Technology, ul. Orshanskaya 3, Moscow, 121552, Russia

Abstract: The generalized Swift–Hohenberg equation with an additional quadratic term is studied. Time-stable localized stationary solutions of the pulse and front types are found. It is shown that stationary fronts give rise to traveling fronts, whose branches are also obtained. This study combines theoretical methods for dynamical systems (in particular, the theory of homo-and heteroclinic orbits) and numerical simulation.

Key words: Swift–Hohenberg evolution equation, stable stationary solutions of the pulse and front types, methods of dynamical systems, numerical simulation.

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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:4, 659–676

Bibliographic databases:

UDC: 519.634
Received: 09.02.2007
Revised: 20.06.2007

Citation: N. E. Kulagin, L. M. Lerman, T. G. Shmakova, “Fronts, traveling fronts, and their stability in the generalized Swift–Hohenberg equation”, Zh. Vychisl. Mat. Mat. Fiz., 48:4 (2008), 693–712; Comput. Math. Math. Phys., 48:4 (2008), 659–676

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Koltsova O., Lerman L., “Hamiltonian dynamics near nontransverse homoclinic orbit to saddle-focus equilibrium”, Discrete Contin. Dyn. Syst., 25:3 (2009), 883–913  crossref  mathscinet  zmath  isi  elib  scopus
    2. Lerman L.M., Markova A.P., “On stability at the Hamiltonian Hopf bifurcation”, Regul. Chaotic Dyn., 14:1 (2009), 148–162  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Kostin D.V., “Initial Boundary Value Problems For Fuss-Winkler-Zimmermann and Swift-Hohenberg Nonlinear Equations of 4Th Order”, Mat. Vestn., 70:1 (2018), 26–39  mathscinet  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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