Existence of solitons in the nonlinear beam equation

This paper concerns with the existence of solitons, namely stable solitary waves in the nonlinear beam equation (NBE) with a suitable nonlinearity. An equation of this type has been introduced by P.J. McKenna and W. Walter as a model of a suspension bridge. We prove both the existence of solitary waves for a large class of nonlinearities and their stability. As far as we know this is the first result about stability of solitary waves in NBE.Comment: 19 page

Solitons in Schr\"odinger-Maxwell equations

In this paper we study the Nonlinear Schr\"odinger-Maxwell equations (NSM). We are interested to analyse the existence of solitons, namely of finite energy solutions which exhibit stability properties. This paper is divided in two parts. In the first, we give an abstract definition of soliton and we develope an abstract existence theory. In the second, we apply this theory to NSM.Comment: arXiv admin note: substantial text overlap with arXiv:1212.323

Hylomorphic solitons on lattices

This paper is devoted to prove the existence of solitons on lattices. We are interested in solitary waves and solitons whose existence is related to the ratio energy/charge. These solitary waves are called hylomorphic. This class includes the Q-balls, which are spherically symmetric solutions of the nonlinear Klein-Gordon equation, as well as solitary waves and vortices which occur, by the same mechanism, in the nonlinear Schroedinger equation and in gauge theories. In this paper we prove an abstract existence theorem which applies to many situations already considered in the literature and also to the nonlinear Schroedinger (and Klein-Gordon) equations defined on a lattice.Comment: 28 page

Hylomorphic solitons and charged Q-balls : existence and stability

In this paper we present a general theoretical framework from which several known results (a some new ones) on the existence and stability of solitons can be recovered. We give an abstract definition of solitary wave and soliton and we develope an abstract existence theory. This theory provides a powerful tool to study the existence of solitons for the Klein-Gordon equations as well as for gauge theories. Applying this theory, we prove the existence of a continuous family of stable charged Q-ball

A minimization method and applications to the study of solitons

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).Comment: arXiv admin note: substantial text overlap with arXiv:1103.113

Existence of hylomorphic solitary waves in Klein-Gordon and in Klein-Gordon-Maxwell equations

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 solitary wave which has a non-vanishing angular momentum is called vortex. We know (at least) three mechanisms which might produce solitary waves and vortices: 1) Complete integrability, (e.g. Kortewg-de Vries equation) 2) Topological constraints, (e.g. Sine-Gordon equation); 3) Ratio energy/charge: (e.g. the nonlinear Klein-Gordon equation). The third type of solitary waves or solitons will be called hylomorphic. This class includes the Q-balls which are spherically symmetric solutions of the nonlinear Klein-Gordon equation (NKG) as well as solitary waves and vortices which occur, by the same mechanism, in the nonlinear Schroedinger equation and in gauge theories. This paper is devoted to an abstract theorem which allows to prove the existence of hylomorphic solitary waves, solitons and vortices in the (NKG) and in the nonlinear Klein-Gordon-Maxwell equations (NKGM