English

A minimization method and applications to the study of solitons

Analysis of PDEs 2011-11-09 v1 Mathematical Physics math.MP

Abstract

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 Schr\"odinger equation (NSE) and to the nonlinear Klein-Gordon equation (NKG).

Keywords

Cite

@article{arxiv.1111.1888,
  title  = {A minimization method and applications to the study of solitons},
  author = {Vieri Benci and Donato Fortunato},
  journal= {arXiv preprint arXiv:1111.1888},
  year   = {2011}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1103.1131