TY - JOUR
T1 - Localized Patterns of the Cubic-Quintic Swift-Hohenberg Equations with Two Symmetry-Breaking Terms
AU - Xu , Yancong
AU - Lan , Tianzhu
AU - Wei , Zhenxue
JO - Annals of Applied Mathematics
VL - 1
SP - 94
EP - 110
PY - 2022
DA - 2022/06
SN - 34
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/aam/20565.html
KW - round-snakes, round-isolas. normal form, Swift-Hohenberg
equation, localized patterns.
AB - <p style="text-align: justify;">Homoclinic snake always refers to the branches of homoclinic orbits near a
heteroclinic cycle connecting a hyperbolic or non-hyperbolic equilibrium and
a periodic orbit in a reversible variational system. In this paper, the normal form of a Swift-Hohenberg equation with two different symmetry-breaking
terms (non-reversible term and non-$k$-symmetry term) are investigated by using multiple scale method, and their bifurcation diagrams are initially studied
by numerical simulations. Typically, we predict numerically the existence of so-called round-snakes and round-isolas upon particular two symmetric-breaking
perturbations.</p>