Ginzburg-Landau-Schrodinger equation

The Ginzburg-Landau-Schrodinger equation is

$iu_{t}^{\epsilon }+\Delta u^{\epsilon }={\frac {1}{\epsilon ^{2}}}(|u^{\epsilon }|^{2}-1)u^{\epsilon }.$

The main focus of study for this equation is the formation of vortices and their dynamics in the limit $\epsilon \to 0$.

The Ginzburg-Landau theory is briefly surveyed on Wikipedia.