Abstract
Some generalizations of the Swift-Hohenberg equation are proposed in order to study the convective patterns that appeal under different conditions. By means of this generalized equation two situations are considered. The first one concerns changes of symmetries in stationary patterns. In the second one a convective pattern under rotation is studied. This effect must be included by a non variational term and the corresponding solutions are not stationary. A detailed analysis of the corresponding amplitude equations is also made in order to compare the results obtained with the generalized Swift-Hohenberg equation. Analytical and numerical methods are used to determine the stability of the corresponding solutions. Simulations of these models can be compared with patterns obtained in recent experiments and suggest some situations in which some new dynamical effects could be obtained.
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