Localized Patterns of the Cubic-Quintic Swift-Hohenberg Equations with Two Symmetry-Breaking Terms

Localized Patterns of the Cubic-Quintic Swift-Hohenberg Equations with Two Symmetry-Breaking Terms

Year:    2018

Author:    Yancong Xu, Tianzhu Lan, Zhenxue Wei

Annals of Applied Mathematics, Vol. 34 (2018), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/2018-AAM-20565

Annals of Applied Mathematics, Vol. 34 (2018), Iss. 1 : pp. 94–110

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    17

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

Author Details

Yancong Xu

Tianzhu Lan

Zhenxue Wei