Variational Methods in Nonlinear Field Equations: Solitary Waves, Hylomorphic Solitons and Vortices

✍ Scribed by Vieri Benci, Donato Fortunato (auth.)

• Publisher: Springer International Publishing
• Year: 2014
• Tongue: English
• Leaves: 266
• Series: Springer Monographs in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

The book analyzes the existence of solitons, namely of finite energy solutions of field equations which exhibit stability properties. The book is divided in two parts. In the first part, the authors give an abstract definition of solitary wave and soliton and we develop an abstract existence theory for hylomorphic solitons, namely for those solitons which minimize the energy for a given charge. In the second part, the authors apply this theory to prove the existence of hylomorphic solitons for some classes of field equations (nonlinear Klein-Gordon-Maxwell equations, nonlinear Schrödinger-Maxwell equations, nonlinear beam equation,..). The abstract theory is sufficiently flexible to be applied to other situations, like the existence of vortices. The books is addressed to Mathematicians and Physicists.

✦ Table of Contents

Front Matter....Pages i-xix
The General Principles....Pages 1-25
Solitary Waves and Solitons: Abstract Theory....Pages 27-59
The Nonlinear Schrödinger Equation....Pages 61-110
The Nonlinear Klein-Gordon Equation....Pages 111-142
The Nonlinear Klein-Gordon-Maxwell Equations....Pages 143-182
The Nonlinear Schrödinger-Maxwell Equations....Pages 183-202
The Nonlinear Beam Equation....Pages 203-218
Vortices....Pages 219-236
Back Matter....Pages 237-253

✦ Subjects

Partial Differential Equations; Analysis; Mathematical Physics