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 results by Berger, Jaffe and Taubes and some of their colleagues touched the nonlinear aspects in great detail. In 1991, a physics seminar...