1,057 research outputs found
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
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
Generalized Functions Beyond Distributions
Ultrafunctions are a particular class of functions defined on a Non
Archimedean field R^{*}\supset R. They have been introduced and studied in some
previous works ([1],[2],[3]). In this paper we introduce a modified notion of
ultrafunction and we discuss sistematically the properties that this
modification allows. In particular, we will concentrated on the definition and
the properties of the operators of derivation and integration of
ultrafunctions.Comment: 29 pages, Keywords: Ultrafunctions, Delta function, distributions,
Non Archimedean Mathematics, Non Standard Analysis. arXiv admin note: text
overlap with arXiv:1302.715
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