This book is concerned with the study in two dimensions of stationary solutions of u
?
of a complex valued Ginzburg-Landau equation involving a small parameter ?. Such problems are related to questions occurring in physics, e.g., phase transition phenomena in superconductors and superfluids. The parameter ? has a dimension of a length which is usually small. Thus, it is of great interest to study the asymptotics as ? tends to zero.
One of the main results asserts that the limit u-star of minimizers u
?
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.
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Illustrationen
1 farbige Abbildung, 4 s/w Abbildungen
XXIX, 159 p. 5 illus., 1 illus. in color.
Dateigröße
ISBN-13
978-3-319-66673-0 (9783319666730)
DOI
10.1007/978-3-319-66673-0
Schweitzer Klassifikation
