2011/11/08 by Vieri Benci, Donato Fortunato, Benci, Vieri +1 · 1 citation
Mathematics · Physics and Astronomy · #35J50 #35Q51 #35Q55 #37K45 #47J30 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.AP #math.MP #msc:35J50 #msc:35Q51 #msc:35Q55 #msc:37K45 #msc:47J30
paper · pdf · doi:10.48550/arxiv.1111.1888
arXiv admin note: substantial text overlap with arXiv:1103.1131
arxiv created 2011/11/08 · openalex publication_date 2011/11/08 · arxiv updated 2011/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Roughly speaking a solitary wave is a solution of a field equation whose energy travels as a localized packet and which preserves this localization in time. A soliton is a solitary wave which exhibits some strong form of stability so that it has a particle-like behavior. In this paper, we prove a general, abstract theorem (Theorem 26) which allows to prove the ex istence of a class of solitons. Such solitons are suitable minimizers of a constrained functional and they are called hylomorphic solitons. Then we apply the abstract theory to problems related to the nonlinear Schrödinger equation (NSE) and to the nonlinear Klein-Gordon equation (NKG).