This article is cited in 7 papers

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

N. E. Kulagin^a, L. M. Lerman^b, T. G. Shmakova<sup>c

a</sup> 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.

UDC: 519.634

Received: 09.02.2007
Revised: 20.06.2007

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

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