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Donato Fortunato

Publications and source records attributed to Donato Fortunato.

14 recordsLinked to original sources
arXiv2016

Existence of torsional solitons in a beam model of suspension bridge

This paper studies the existence of solitons, namely stable solitary waves, in a suspension bridge. The bridge is modeled as a degenerate plate, that is, a central beam with cross sections, and displays two degrees of freedom: the vertical displacement of the beam and the torsional angles of the cross sections. Under fairy general assumptions, we prove the existence of solitons. Under the additional assumption of large tension in the sustaining cables, we prove that these solitons have a nontrivial torsional component. This appears relevant for the security since several suspension bridges collapsed due to torsional oscillations.

math.AP↗
arXiv2014

Hylomorphic solitons for the generalized KdV equation

In this paper we prove the existence of hylomorphic solitons in the generalized KdV equation. A soliton is called hylomorphic if it is a solitary wave whose stability is due to a particular relation between energy and another integral of motion which we call hylenic charge.

math-ph↗
arXiv2013

Solitons in Schrödinger-Maxwell equations

In this paper we study the Nonlinear Schrödinger-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.

math.AP↗
arXiv2012

Hylomorphic solitons and charged Q-balls: existence and stability

In this paper we give an abstract definition of solitary wave and soliton and we develop 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-balls.

math-ph↗
arXiv2011

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 Schrödinger equation (NSE) and to the nonlinear Klein-Gordon equation (NKG).

math.AP↗
arXiv2011

An abstract theorem on the existence of hylomorphic solitons

In this paper we prove an abstract theorem which can be used to study the existence of solitons for various dynamical systems described by partial differential equations. We also give an idea of how the abstract theorem can be applied to prove the existence of solitons in some dynamical systems.

math.AP↗
arXiv2011

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.

math.AP↗
arXiv2010

On the existence of stable charged Q-balls

This paper concerns hylomorphic solitons, namely stable, solitary waves whose existence is related to the ratio energy/charge. In theoretical physics, the name Q-ball refers to a type of hylomorphic solitons or soli- tary waves relative to the Nonlinear Klein-Gordon equation (NKG). We are interested in the existence of charged Q-balls, namely Q-balls for the Nonlinear Klein-Gordon equation coupled with the Maxwell equations (NKGM). In this case the charge reduces to the electric charge. The main result of this paper establishes that stable, charged Q-balls exist provided that the interaction between matter and the gauge field is sufficiently small.

math-ph↗
arXiv2010

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.

math.AP↗
arXiv2009

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)

math.AP↗
arXiv2009

Hylomorphic Vortices in Abelian Gauge Theories

We consider an Abelian Gauge Theory in R4 equipped with the Minkowski metric. This theory leads to a system of equations, the Klein-Gordon- Maxwell equations, which provide models for the interaction between the electromagnetic field and matter. We assume that the nonlinear term is such that the energy functional is positive; this fact makes the theory more suitable for physical models. A three dimensional vortex is a finite energy, stationary solution of these equations such that the matter field has nontrivial angular momen- tum and the magnetic field looks like the field created by a finite solenoid. Under suitable assumptions, we prove the existence of three dimensional vortex-solutions.

math-ph↗
arXiv2007

Three dimensional vortices in Abelian Gauge Theories

In this paper we consider an Abelian Gauge Theory in R^4 equipped with the Minkowski metric. This theory leads to a system of equations, the Klein-Gordon-Maxwell equations, which provide models for the interaction between the electromagnetic field and matter. A three dimensional vortex is a finite energy solution of these equations in which the magnetic field looks like the field created by a finite solenoid. Under suitable assumptions, we prove the existence of vortex-solutions.

math.AP↗
arXiv2007

Solitary waves in Abelian Gauge Theories

Abelian gauge theories consist of a class of field equations which provide a model for the interaction between matter and electromagnetic fields. In this paper we analyze the existence of solitary waves for these theories. We assume that the lower order term W is positive and we prove the existence of solitary waves if the coupling between matter and electromagnetic field is small. We point out that the positiveness assumption on W implies that the energy is positive: this fact makes these theories more suitable to model physical phenomena.

math.AP↗