Hylomorphic solitons

This paper is devoted to the study of 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 (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 the study of hylomorphic soliton. Mainly we will be interested in the very general principles which are at the base of their existence such as the Variational Principle, the Invariance Principle, the Noether theorem, the Hamilton-Jacobi theory etc. We give a general definition of hylomorphic solitons and an interpretation of their nature (swarm interpretation) which is very helpful in understanding their behavior. We apply these ideas to the Nonlinear Schroedinger Equation (NS) and to the Nonlinear Klein-Gordon Equation (NKG) repectively

Geodesic connectedness and conjugate points in GRW spacetimes

Given two points of a Generalized Robertson-Walker spacetime, the existence, multiplicity and causal character of geodesic connecting them is characterized. Conjugate points of such geodesics are related to conjugate points of geodesics on the fiber, and Morse-type relations are obtained. Applications to bidimensional spacetimes and to GRW spacetimes satisfying the timelike convergence condition are also found.Comment: 31 pages and 2 figure

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

Solitary waves and vortices in non-Abelian gauge theories with matter

We consider a non-Abelian gauge theory in R^{4} equipped with the Minkowski metric, which provides a model for the interaction between a bosonic matter field and a gauge field with gauge group SU(2). We prove the existence of solitary waves which are related to those found for the Klein-Gordon-Maxwell equations.Comment: 15 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