Rubinstein, Jacob Self-induced motion of line defects. (English) Zbl 0728.35118 Q. Appl. Math. 49, No. 1, 1-9 (1991). Summary: The evolution of the 2-d Ginzburg-Landau functional under the Schrödinger and the diffusion dynamics is considered. We construct solutions u(x,t), \(u\in {\mathbb{R}}^ 2\), \(x\in {\mathbb{R}}^ 3\), such that the vector field u vanishes along a singular curve \(\gamma\). Equations of motion for \(\gamma\) (t) are derived by the method of matched asymptotic expansions. Cited in 5 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) Keywords:nonlinear Schrödinger-Ginzburg-Landau equation PDFBibTeX XMLCite \textit{J. Rubinstein}, Q. Appl. Math. 49, No. 1, 1--9 (1991; Zbl 0728.35118) Full Text: DOI