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| LOCALIZED PATTERNS OF THE SWIFT-HOHENBERG EQUATION WITH A DISSIPATIVE TERM |
| Yongli Liu,Yancong Xu |
| (Dept. of Math., Hangzhou Normal University, Hangzhou 310036, Zhejiang, PR China) |
| DOI： |
| Abstract: |
| In this paper, the normal form analysis of quadratic-cubic Swift-Hohenberg equation with a dissipative term is investigated by using the multiple-scale method. In addition, we obtain Hamiltonian-Hopf bifurcations of two equilibria and homoclinic snaking bifurcations of one-peak and two-peak homoclinic solutions by numerical simulations. |
| Key words: bifurcation; normal form; Swift-Hohenberg equation; Hamiltonian-Hopf; snakes |