Ginzburg-Landau Patterns in Circular and Spherical Geometries: Vortices, Spirals, and Attractors

Author(s)

Dai, Jia-Yuan ^{[1, 2]} ; Lappicy, Phillipo ^{[3, 4]}

Affiliation

^[1] Natl Chung Hsing Univ, Dept Appl Math, Taichung 402 - Taiwan

^[2] Natl Taiwan Univ, Natl Ctr Theoret Sci, Taipei 106 - Taiwan

^[3] Univ Lisbon, Inst Super Tecn, P-1049001 Lisbon - Portugal

^[4] Univ Sao Paulo, ICMC, BR-13566590 Sao Carlos, SP - Brazil

• Document type: Journal article
• Source: SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS; v. 20, n. 4, p. 1959-1984, 2021.
• Web of Science Citations: 0

Abstract

This paper consists of three results on pattern formation of Ginzburg-Landau m-armed vortex solutions and spiral waves in circular and spherical geometries. First, we completely describe the global bifurcation diagram of vortex equilibria. Second, we prove persistence of all bifurcation curves under perturbations of parameters, which yields the existence of spiral waves for the complex Ginzburg-Landau equation. Third, we explicitly construct the global attractor of m-armed vortex solutions. Our main tool is a new shooting method that allows us to prove hyperbolicity of vortex equilibria in the invariant subspace of vortex solutions. (AU)

• FAPESP's process: 18/18703-1 - Attractors for fully nonlinear parabolic equations and non-autonomous equations
• Grantee: Phillipo Lappicy Lemos Gomes
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 17/07882-0 - Einstein constraints and differential equations on the sphere
• Grantee: Phillipo Lappicy Lemos Gomes
• Support Opportunities: Scholarships in Brazil - Post-Doctoral