Self-induced motion of line defects

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Abstract
The evolution of the 2-d Ginzburg-Landau functional under the Schrodinger and the diffusion dynamics is considered. We construct solutions u ( x , t ) , u ∈ R 2 , x ∈ R 3 u\left ( {x, t} \right ), u \in {R^2}, x \in {R^3} , such that the vector field u u vanishes along a singular curve γ \gamma . Equations of motion for γ ( t ) \gamma \left ( t \right ) are derived by the method of matched asymptotic expansions.

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