Ginzburg-Landau Spiral Waves in Circular and Spherical Geometries

2020/10/24 by Jia-Yuan Dai · 1 citation
Mathematics · #math.AP #math.DS

paper · pdf · doi:10.1137/19m1300145

published as SIAM Journal on Mathematical Analysis 53(1) (2021):1004-1028 · 25 pages, 4 figures

arxiv created 2020/10/24 · arxiv updated 2021/02/24

Abstract

We prove the existence of m-armed spiral wave solutions for the complex Ginzburg-Landau equation in the circular and spherical geometries. We establish a new global bifurcation approach and generalize the results of existence for rigidly-rotating spiral waves. Moreover, we prove the existence of two new patterns: frozen spirals in the circular and spherical geometries, and 2-tip spirals in the spherical geometry.

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