LOCALIZED PATTERNS OF THE CUBIC-QUINTIC SWIFT-HOHENBERG EQUATIONS WITH TWO SYMMETRY-BREAKING TERMS |
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| Authors: | Yancong Xu Tianzhu Lan and Zhenxue Wei |
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| Institution: | Dept. of Math., Hangzhou Normal University, Hangzhou 310036, Zhejiang, PR China,Dept. of Math., Hangzhou Normal University, Hangzhou 310036, Zhejiang, PR China and School of Computer Science and Software Engineering, East China Normal University, 200062, Shanghai, PR China |
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| Abstract: | Homoclinic snake always refers to the branches of homoclinic orbits \mbox{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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| Keywords: | round-snakes round-isolas normal form Swift-Hohenberg equation localized patterns |
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