{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,18]],"date-time":"2026-01-18T06:46:51Z","timestamp":1768718811888,"version":"3.49.0"},"reference-count":29,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p> We study a model equation that mimics convection under rotation in a fluid with temperature-dependent properties (non-Boussinesq (NB)), high Prandtl number and idealized boundary conditions. It is based on a model equation proposed by Segel [1965] by adding rotation terms that lead to a K\u00fcppers\u2013Lortz instability [K\u00fcppers &amp; Lortz, 1969] and can develop into oscillating hexagons. We perform a weakly nonlinear analysis to find out explicitly the coefficients in the amplitude equation as functions of the rotation rate. These equations describe hexagons and oscillating hexagons quite well, and include the Busse\u2013Heikes (BH) model [Busse &amp; Heikes, 1980] as a particular case. The sideband instabilities as well as short wavelength instabilities of such hexagonal patterns are discussed and the threshold for oscillating hexagons is determined. <\/jats:p>","DOI":"10.1142\/s0218127404009107","type":"journal-article","created":{"date-parts":[[2004,3,12]],"date-time":"2004-03-12T08:57:28Z","timestamp":1079081848000},"page":"107-117","source":"Crossref","is-referenced-by-count":4,"title":["HEXAGONAL PATTERNS IN A MODEL FOR ROTATING CONVECTION"],"prefix":"10.1142","volume":"14","author":[{"given":"S.","family":"MADRUGA","sequence":"first","affiliation":[{"name":"Instituto de F\u00edsica, Universidad de Navarra, E-31080 Pamplona, Navarra, Spain"},{"name":"Institut de Physique, Universit\u00e9 de Li\u00e8ge, B5, Sart-Tilman, B-4000 Li\u00e8ge, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"P\u00c9REZ-GARC\u00cdA","sequence":"additional","affiliation":[{"name":"Instituto de F\u00edsica, Universidad de Navarra, E-31080 Pamplona, Navarra, Spain"},{"name":"Depto. Ingenier\u00eda Mec\u00e1nica, E. T. S. Ingenieros (TECNUN), Universidad de Navarra, E-20018 San Sebasti\u00e1n, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.76.756"},{"key":"rf2","first-page":"R4869","volume":"55","author":"Bajaj K. M. S.","journal-title":"Phys. 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Energy Engineering Sciences (Office of Basic Energy Sciences, Department of Energy, USA, 2000)\u00a0pp. 161\u2013168."},{"key":"rf24","first-page":"046219","volume":"65","author":"Roxin A.","journal-title":"Phys. Rev."},{"key":"rf25","first-page":"124","volume":"144","author":"Sain F.","journal-title":"Physica"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112065000228"},{"key":"rf27","first-page":"227","volume":"14","author":"Soward A. 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