×

Self-induced motion of line defects. (English) Zbl 0728.35118

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.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
PDFBibTeX XMLCite
Full Text: DOI