Work

Quantization effects for multi-component Ginzburg-Landau vortices

Year: 2025

Type: article

Abstract: In this paper, we are concerned with n -component Ginzburg-Landau equations on R 2 ${\mathbb{R}}^{2}$ . By introducing a diffusion constant for each component, we discuss that the n -component equations are different from n -copies of the single Ginzburg-Landau equations. Then, the results of Brezis-Merle-Riviere for the single Ginzburg-Landau equation can be nontrivially extended to the multi-component case. First, we show that if the solutions have their gradients in L 2 space, they are trivial solutions. Second, we prove that if the potential is square summable, then it has quantized integrals, i.e., there exists one-to-one correspondence between the possible values of the potential energy and N n ${\mathbb{N}}^{n}$ . Third, we show that different diffusion coefficients in the system are important to obtain nontrivial solutions of n -component equations.

Source: Advanced Nonlinear Studies

DOI: 10.1515/ans-2023-0165

Authors: Rejeb Hadiji, Jongmin Han, Juhee Sohn