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Localized patterns for the quintic complex Swift-Hohenberg equation

✍ Scribed by Hidetsugu Sakaguchi; Helmut R. Brand

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
780 KB
Volume
117
Category
Article
ISSN
0167-2789

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✦ Synopsis

We show using numerical simulations that a variety of localized patterns arise in a model equation: the quintic Swift-Hohenberg equation with complex coefficients. We demonstrate that various sizes of localized standing wave patterns are possible when the imaginary part of the complex coefficient is small. Localized traveling waves as well as localized standing waves with a fixed size are observed when the imaginary part is rather large. We also present stable localized patterns in two spatial dimensions and study their interaction.

📜 SIMILAR VOLUMES

Abundance of stable stationary localized
Abundance of stable stationary localized solutions to the generalized 1D Swift-Hohenberg equation
✍ L.A. Belyakov; L.Yu. Glebsky; L.M. Lerman 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 999 KB

A number of stationary localized solutions to the well-known pattern-forming gradient system mentioned in the title have been found. Their search is based on the theory of homoclinic orbits to a saddle-focus equilibrium and some results of linear symmetric differential operators with decaying coeffi