The Ginzburg–Landau partial differential equation has been used to study a wide range of phenomena including superconductivity, superﬂuidity, chemical patterns, nonlinear oscillations, liquid crystals, and relativistic strings.
The equation has the form
with parameters , . The initial values include two peaks of the form , where is the separation between them.
 H. Brézis and T. Li, Ginzburg–Landau Vortices, Singapore: World Scientific, 2005.