This book is concerned with the study in two dimensions of stationary solutions of u_e of a complex valued Ginzburg-Landau equation involving a small parameter e. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter e has a dimension of a length which is usually small.  Thus, it is of great interest to study the asymptotics as e tends to zero.

One of the main results asserts that the limit u-star of minimizers u_e exists. Moreover, u-star is smooth except at a finite number of points called defects or vortices in physics. The number of these defects is exactly the Brouwer degree - or winding number - of the boundary condition. Each singularity has degree one - or as physicists would say, vortices are quantized.

The material presented in this book covers mostly original results by the authors. It assumes a moderate knowledge of nonlinear functional analysis,partial differential equations, and complex functions. This book is designed for researchers and graduate students alike, and can be used as a one-semester text. The present softcover reprint is designed to make this classic text available to a wider audience.

Affordable, softcover reprint of a classic textbook

Authors are well-known specialists in nonlinear functional analysis and partial differential equations

Written in a clear, readable style with many examples