Variational Methods in Nonlinear Field Equations

Solitary Waves, Hylomorphic Solitons and Vortices
2014
ISBN: 978-3-319-06913-5
Verlag: Springer International Publishing

Buch, Englisch, 253 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 5384 g

Reihe: Springer Monographs in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Fortunato, Donato

Benci, Vieri

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis

Inhaltsverzeichnis

1 The general principles.- 2 Solitary waves and solitons: abstract theory.- 3 The nonlinear Schrödinger equation.- 4 The nonlinear Klein-Gordon equation.- 5 The Nonlinear Klein-Gordon-Maxwell equations.- 6 The nonlinear Schrödinger-Maxwell equations.- 7 The nonlinear beam equation.- 8 Vortices.- 9 Appendix.