We show using numerical simulations that a variety of localized patter
ns arise in a model equation: the quintic Swift-Hohenbeg equation with
complex coefficients. We demonstrate that various sizes of localized
standing wave patterns are possible when the imaginary part of the com
plex coefficient is small. Localized traveling waves as well as locali
zed standing waves with a fixed size are observed when the imaginary p
art is rather large. We also present stable localized patterns in two
spatial dimensions and study their interaction. Copyright (C) 1998 Els
evier Science B.V.