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＜E-Book＞
Variational Methods in Nonlinear Field Equations : Solitary Waves, Hylomorphic Solitons and Vortices / by Vieri Benci, Donato Fortunato
(Springer Monographs in Mathematics. ISSN:21969922)

Edition	1st ed. 2014.
Publisher	Cham : Springer International Publishing : Imprint: Springer
Year	2014
Language	English
Size	XIX, 253 p : online resource
Authors	*Benci, Vieri author Fortunato, Donato author SpringerLink (Online service)
Subjects	LCSH:Differential equations LCSH:Mathematical analysis LCSH:Mathematical physics FREE:Differential Equations FREE:Analysis FREE:Mathematical Physics
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-06914-2

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