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- W2022065360 abstract "In this paper we study a simplified model of the stationary Swift–Hohenberg equation, where the cubic nonlinearity is replaced by a piecewise linear function with similar properties. The main goal is to prove the existence of so-called localized solutions of this equation, i.e., solutions decaying to a homogeneous zero state with unbounded increase of the space variable. The following two cases of the space variable are considered: one-dimensional (on the whole line) and two-dimensional; in the latter case, radially symmetric solutions are studied. The existence of such solutions and increase of their number with change in the equation parameters are shown." @default.
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- W2022065360 date "2014-10-01" @default.
- W2022065360 modified "2023-09-26" @default.
- W2022065360 title "Localized Solutions of a Piecewise Linear Model of the Stationary Swift–Hohenberg Equation on the Line and on the Plane" @default.
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- W2022065360 doi "https://doi.org/10.1007/s10958-014-2072-z" @default.
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