Localized Patterns of the Swift-Hohenberg Equation with a Dissipative Term

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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.

Keywords:

bifurcation normal form Swift-Hohenberg equation Hamiltonian-Hopf snakes.
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