Solitons in Field Theory and Nonlinear Analysis [Paperback]

There are two approaches in the study of differential equations of field theory. The first, finding closed-form solutions, works only for a narrow category of problems. Written by a well-known active researcher, this book focuses on the second, which is to investigate solutions using tools from modern nonlinear analysis.

Preface * Primer of Field Theory * Sigma Models * Multiple Instantons and Characteristic Classes * Generalized Abelian Higgs Equations * Chern-Simons Systems: Abelian Case * Chern-Simons Systems: Non-Abelian Case * Electroweak Vortices * Dyons * Ordinary Differential Equations * Strings in Cosmology * Vortices and Antivortices * Born-Infeld Solutions * References * Bibliography * Index

From the reviews:

Solitons in field theory and nonlinear analysis present a thorough analysis of many different parts in field theory. ... For the enthusiastic, there are some open problems to think about at the end of each chapter. Solitons in field theory and nonlinear analysis is a solid research monograph with a lot of information in it and should certainly stimulate those who already have some background in field theory and analysis. (C. Gilson, Proceedings of the Edinburgh Mathematical Society, Vol. 47, 2004)

A particularly interesting feature of many non-linear systems is the existence of solitons ... . This monograph is mainly devoted to them. Included here there are many important examples of such systems ... . many results are formulated in the language of theorems and their proofs, as it is standard in the mathematical literature. Individual chapters end with notes containing open problems for research. ... The material should be of interest to mathematicians and mathematical physicists at postgraduate level. (European Mathematical Society Newsletter, September, 2003)

The purpose of this book is to give a rather extensive account on solition type solutions in various gaugeló½