Variational Methods in Nonlinear Field Equations

Solitary Waves, Hylomorphic Solitons and Vortices

Vieri Benci, Donato Fortunato (Autoren)

Buch | Softcover

XIX, 253 Seiten

2016 | Softcover reprint of the original 1st ed. 2014
Springer International Publishing (Verlag)
978-3-319-36122-2 (ISBN)

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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.

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.

"This book is a useful, enlightening, and thought-provoking exposition of the research and findings over the last 35 years of using and implementing variational techniques to better understand the dynamics of nonlinear field equations. These reviewers would highly recommend this text be on the shelf of any applied mathematician/physicist who uses variational techniques to analyze nonlinear field equations." (David J. Kaup and Thomas Keith Vogel, Mathematical Reviews, November, 2015)

Erscheinungsdatum	29.08.2016
Reihe/Serie	Springer Monographs in Mathematics
Zusatzinfo	XIX, 253 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Naturwissenschaften ► Physik / Astronomie
Schlagworte	Analysis • Calculus and mathematical analysis • Differential calculus and equations • Mathematical Physics • mathematics and statistics • Partial differential equations • Solitons • symmetry • Variational • Vortices
ISBN-10	3-319-36122-8 / 3319361228
ISBN-13	978-3-319-36122-2 / 9783319361222
Zustand	Neuware