The theory of complex Ginzburg-Landau type phase transition and its applica- tions to superconductivity and superfluidity has been a topic of great interest to theoretical physicists and has been continuously and persistently studied since the 1950s. Today, there is an abundance of mathematical results spread over numer- ous scientific journals. However, before 1992, most of the studies concentrated on formal asymptotics or linear analysis. Only isolated...