Localized Patterns of the Swift-Hohenberg Equation with a Dissipative Term
Keywords:
bifurcation, normal form, Swift-Hohenberg equation, Hamiltonian-Hopf, snakes.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.