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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2008, Volume 48, Number 4, Pages 693–712 (Mi zvmmf159)  
This article is cited in 6 scientific papers (total in 6 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
Full-text PDF (2530 kB) Citations (6)
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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.
Received: 09.02.2007
Revised: 20.06.2007
English version:
Computational Mathematics and Mathematical Physics, 2008, Volume 48, Issue 4, Pages 659–676
DOI: https://doi.org/10.1134/S0965542508040131
Bibliographic databases:
Document Type: Article
UDC: 519.634
Language: Russian
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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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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