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D. N. Migranova¹, R. N. Ismagilova^2,3, N. G. Migranov⁴, D. V. Kondratyev^5,6

Author affiliations
¹Eastern Economics and Law Humanities Academy,
3 Mubarjakova St., Ufa, 450092, Russia
²LLC "BashNIPIneft",
86/1 Lenin St., Ufa, 450006, Russia
³Bashkir State Pedagogical University,
3a October revolution St., Ufa, 450000, Russia
⁴Institute of Mechanics Ufa Research Centre RAS,
71 October Av., Ufa, 450008, Russia
⁵Academy of Sciences of Republic Bashkortostan,
15 Kirov St., Ufa, 450008, Russia
⁶Bashkir Cooperative Institute (branch) of the Russian Cooperative University,
26 Lenin St., Ufa, 450000, Russia
E-mail: denis.kondratyev@bk.ru

Abstract
A system of nonlinear differential equations describing surface stabilized ferroelectric liquid crystal SmC* in the chevron’s geometry in the framework of continual model is considered. The purpose of this work is obtaining of new solutions describing the appearance of chevrons. It is shown that the solution expressed through the elliptic functions allows to explain the appearance and structure of chevrons. The energy of the ferroelectric liquid crystal is estimated using the solution expressed in terms of the elliptical sine.

Keywords: mathematical modeling, ferroelectric liquid crystal, smectic layer, chevron