286 research outputs found
Shock-peakon and shock-compacton solutions for K(p,q) equation by variational iteration method
AbstractBy variational iteration method, we obtain new solitary solutions for non-linear dispersive equations. Particularly, shock-peakon solutions in K(2,2) equation and shock-compacton solutions in K(3,3) equation are found by this simple method. These two types of solutions are new solitary wave solutions which have the shapes of shock solutions and compacton solutions (or peakon solutions)
Spontaneous symmetry breaking, and strings defects in hypercomplex gauge field theories
Inspired by the appearance of split-complex structures in the dimensional
reduction of string theory, and in the theories emerging as byproducts, we
study the hyper-complex formulation of Abelian gauge field theories, by
incorporating a new complex unit to the usual complex one. The hypercomplex
version of the traditional Mexican hat potential associated with the
gauge field theory, corresponds to a {\it hybrid} potential with two real
components, and with as symmetry group. Each component
corresponds to a deformation of the hat potential, with the appearance of a new
degenerate vacuum. Hypercomplex electrodynamics will show novel properties,
such as the spontaneous symmetry breaking scenarios with running masses for the
vectorial and scalar Higgs fields, and the Aharonov-Bohm type strings defects
as exact solutions; these topological defects may be detected only by quantum
interference of charged particles through gauge invariant loop integrals. In a
particular limit, the {\it hyperbolic} electrodynamics does not admit
topological defects associated with continuous symmetriesComment: 40 page
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Nonlinear Partial Differential Equations on Graphs
One-dimensional metric graphs in two and three-dimensional spaces play an important role in emerging areas of modern science such as nano-technology, quantum physics, and biological networks. The workshop focused on the analysis of nonlinear partial differential equations on metric graphs, especially on the bifurcation and stability of nonlinear waves on complex graphs, on the justification of Kirchhoff boundary conditions, on spectral properties and the validity of amplitude equations for periodic graphs, and the existence of ground states for the NLS equation with and without potential
Dynamical Boson Stars
The idea of stable, localized bundles of energy has strong appeal as a model
for particles. In the 1950s John Wheeler envisioned such bundles as smooth
configurations of electromagnetic energy that he called {\em geons}, but none
were found. Instead, particle-like solutions were found in the late 1960s with
the addition of a scalar field, and these were given the name {\em boson
stars}. Since then, boson stars find use in a wide variety of models as sources
of dark matter, as black hole mimickers, in simple models of binary systems,
and as a tool in finding black holes in higher dimensions with only a single
killing vector. We discuss important varieties of boson stars, their dynamic
properties, and some of their uses, concentrating on recent efforts.Comment: 79 pages, 25 figures, invited review for Living Reviews in
Relativity; major revision in 201
Exact closed form solutions of compound Kdv Burgers’ equation by using generalized (Gʹ/G) expansion method
In this investigation, the compound Korteweg-de Vries (Kd-V) Burgers equation with constant coefficients is considered as the model, which is used to describe the properties of ion-acoustic waves in plasma physics, and also applied for long wave propagation in nonlinear media with dispersion and dissipation. The aim of this paper to achieve the closed and dynamic closed form solutions of the compound KdV Burgers equation. We derived the completely new solutions to the considered model using the generalized (Gʹ/G)-expansion method. The newly obtained solutions are in form of hyperbolic and trigonometric functions, and rational function solutions with inverse terms of the trigonometric, hyperbolic functions. The dynamical representations of the obtained solutions are shown as the annihilation of three-dimensional shock waves, periodic waves, and multisoliton through their three dimensional and contour plots. The obtained solutions are also compared with previously exiting solutions with both analytically and numerically, and found that our results are preferable acceptable compared to the previous results.Publisher's Versio
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