TY - JOUR
T1 - Localized patterns for the quintic complex Swift-Hohenberg equation
AU - Sakaguchi, Hidetsugu
AU - Brand, Helmut R.
N1 - Funding Information:
HRB thanks the Deutsche Forschungsgemeinschaft for partial support of this work through the German-Japanese cooperative research project 'Nonlinear Waves and Interfaces'.
PY - 1998
Y1 - 1998
N2 - 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.
AB - 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.
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U2 - 10.1016/S0167-2789(97)00310-2
DO - 10.1016/S0167-2789(97)00310-2
M3 - Article
AN - SCOPUS:0001838980
SN - 0167-2789
VL - 117
SP - 95
EP - 105
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 1-4
ER -