03676nam 22007095 450 991029997280332120220218135121.03-319-06914-410.1007/978-3-319-06914-2(CKB)3710000000268420(EBL)1964665(OCoLC)896848824(SSID)ssj0001372827(PQKBManifestationID)11780043(PQKBTitleCode)TC0001372827(PQKBWorkID)11314196(PQKB)11150461(MiAaPQ)EBC1964665(DE-He213)978-3-319-06914-2(PPN)182098532(EXLCZ)99371000000026842020141024d2014 u| 0engur|n|---|||||txtccrVariational Methods in Nonlinear Field Equations Solitary Waves, Hylomorphic Solitons and Vortices /by Vieri Benci, Donato Fortunato1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (266 p.)Springer Monographs in Mathematics,1439-7382Description based upon print version of record.3-319-06913-6 Includes bibliographical references.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.Springer Monographs in Mathematics,1439-7382Differential equations, PartialMathematical analysisCalculusMathematical physicsPartial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12007Mathematical Physicshttps://scigraph.springernature.com/ontologies/product-market-codes/M35000Differential equations, Partial.Mathematical analysis.Calculus.Mathematical physics.Partial Differential Equations.Analysis.Mathematical Physics.510515515.353530.15Benci Vieriauthttp://id.loc.gov/vocabulary/relators/aut66367Fortunato Donatoauthttp://id.loc.gov/vocabulary/relators/autBOOK9910299972803321Variational Methods in Nonlinear Field Equations2499260UNINA