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Volume 34, Issue 1
Localized Patterns of the Cubic-Quintic Swift-Hohenberg Equations with Two Symmetry-Breaking Terms

Yancong Xu, Tianzhu Lan & Zhenxue Wei

Ann. Appl. Math., 34 (2018), pp. 94-110.

Published online: 2022-06

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  • Abstract

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.

  • Keywords

round-snakes, round-isolas. normal form, Swift-Hohenberg equation, localized patterns.

  • AMS Subject Headings

37G25, 37G20, 37C29

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAM-34-94, author = {Xu , YancongLan , Tianzhu and Wei , Zhenxue}, title = {Localized Patterns of the Cubic-Quintic Swift-Hohenberg Equations with Two Symmetry-Breaking Terms}, journal = {Annals of Applied Mathematics}, year = {2022}, volume = {34}, number = {1}, pages = {94--110}, abstract = {

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.

}, issn = {}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/aam/20565.html} }
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 -

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.

Yancong Xu, Tianzhu Lan & Zhenxue Wei. (2022). Localized Patterns of the Cubic-Quintic Swift-Hohenberg Equations with Two Symmetry-Breaking Terms. Annals of Applied Mathematics. 34 (1). 94-110. doi:
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