Related papers: Space-time noncommutativity and (1+1) Higgs Model
Using the concentration-compactness method and the localized virial type arguments, we study the behavior of $H^1$ solutions to the focusing quintic NLS in $\R^2$, namely, $$i \partial_t u+\Delta u+|u|^4u=0,\quad\quad (x, t) \in…
A complete cosmological evolution model of the classical scalar field with a Higgs potential is studied and simulated on a computer without the assumption that the Hubble constant is nonnegative. It is shown that with most initial…
We derive a non-linear sigma-model for the transport of light (classical waves) through a disordered medium. We compare this extension of the model with the well-established non-linear sigma-model for the transport of electrons…
Based on the observation that the exterior space-times of Schwarzschild-type solutions allow two symmetric slicings, a static spherically symmetric one and a timelike homogeneous one, modifications of gravitational dynamics suggested by…
We compare two different models of transport of light in a disordered system with a spherical Gaussian distribution of scatterers. A coupled dipole model, keeping into account all interference effects, is compared to an incoherent model,…
The classical scattering of cylindrical gravitational waves is exactly solvable. The motivation for this paper is to understand if the quantum scattering problem is also exactly solvable. The classical dynamics is governed by a two…
We extend the non-commutative coordinates relationship into other than the Minkowski space-time. We clarify the non-commutativity dependency to the geometrical structure. As well as, we find an inverse map between Riemann's normal and…
We study a scalar field model in a two dimensional space-time with a generalized $\phi^4_G$ potential which has four minima, obtaining novel kink solutions with well defined properties although the potential is non-analytical at the origin.…
Multidimensional cosmological models with $n~(n > 1)$ Einstein spaces are discussed classically and with respect to canonical quantization. These models are integrable in the case of Ricci flat internal spaces. For negative curvature of the…
We investigate scattering properties of a Moyal deformed version of the nonlinear Schr\"odinger equation in an even number of space dimensions. With rather weak conditions on the degree of nonlinearity, the Cauchy problem for general…
In this work we consider kink-antikink collisions for some classes of $(1,1)$-dimensional nonlinear models. We are particularly interested to investigate in which aspect the presence of a general kinetic content in the Lagrangian could be…
We identify the kinks of a deformed O(3) linear Sigma model as the solutions of a set of first-order systems of equations; the above model is a generalization of the MSTB model with a three-component scalar field. Taking into account…
We construct a scattering theory for harmonic one-forms on Riemann surfaces, obtained from boundary value problems through systems of curves and the jump problem. We obtain an explicit expression for the scattering matrix in terms of…
A non-commutative differential calculus on the $h$-superplane is presented via a contraction of the $q$-superplane. An R-matrix which satisfies both ungraded and graded Yang-Baxter equations is obtained and a new deformation of the $(1+1)$…
A first order equation for a static ${\phi}^4$ kink in the presence of an impurity is extended into an iterative scheme. At the first iteration, the solution is the standard kink, but at the second iteration the kink impurity generates a…
An unified structure of noncommutative space-time for both gravity and particle physics is presented. This gives possibilities of testing the idea of noncommutative space-time at the currently available energy scale. There are several…
A new approach to the quantization of the relativistic kink - model around the solitonic solution is developed on the ground of the collective coordinates method. The corresponding effective action is proved to be the action of the…
We study the Quantum-Mechanics on the hyper-Kahler manifold that is the blow-up of an $A_1$-singularity. This system is relevant for M(atrix)-theory as it was conjectured to describe scattering in the "noncommutative" deformation of a free…
We prove short-time existence of smooth solutions for a class of nonlinear, and in general spatially nonlocal, Hamiltonian evolution equations that describe the self-interaction of weakly nonlinear scale-invariant waves. These equations…
We study the cubic-quintic NLS in three space dimensions. It is known that scattering holds for solutions with mass-energy in a region corresponding to positive virial, the boundary of which is delineated both by ground state solitons and…