Dynamic bifurcation of the \(n\)-dimensional complex Swift-Hohenberg equation. (English) Zbl 1203.35277
Summary: This paper is concerned with the bifurcation of a complex Swift-Hohenberg equation. The attractor bifurcation of the complex Swift-Hohenberg equation on a one-dimensional domain \((0,L)\) is investigated. It is shown that the \(n\)-dimensional complex Swift-Hohenberg equation bifurcates from the trivial solution to an attractor under the Dirichlet boundary condition on a general domain and under a periodic boundary condition when the bifurcation parameter crosses some critical values. The stability property of the bifurcation attractor is analyzed.
MSC:
| 35Q60 | PDEs in connection with optics and electromagnetic theory |
| 35B32 | Bifurcations in context of PDEs |
| 70K50 | Bifurcations and instability for nonlinear problems in mechanics |
| 37L10 | Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems |
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