H. Sakaguchi et Hr. Brand, STANDING-WAVE LOCALIZED SQUARES IN PATTERN-FORMING NONEQUILIBRIUM SYSTEMS, Journal de physique. II, 7(10), 1997, pp. 1325-1330
We show that stable standing wave localized solutions of square symmet
ry are possible for a quintic Swift-Hohenberg type equation with compl
ex coefficients. We point out that these localized solutions, which ar
e surrounded by a pattern-free state exist for a range of values for t
he external stress parameter subcritically. We discuss similarities to
recent experimental observations of standing wave localized squares i
n granular materials.