The Bullough-Dodd model coupled to matter fields

The Bullough-Dodd model is an important two-dimensional integrable field theory which finds applications in physics and geometry. We consider a conformally invariant extension of it, and study its integrability properties using a zero curvature condition based on the twisted Kac-Moody algebra A(2)((2)). The one- and two-soliton solutions as well as the breathers are constructed explicitly. We also consider integrable extensions of the Bullough-Dodd model by the introduction of spinor (matter) fields. The resulting theories are conformally invariant and present local internal symmetries. All the one-soliton solutions, for two examples of those models, are constructed using a hybrid of the dressing and Hirota methods. One model is of particular interest because it presents a confinement mechanism for a given conserved charge inside the solitons. (C) 2008 Elsevier B.V. All rights reserved.

SOME COMMENTS ON QUASI-INTEGRABILITY

In this paper we present our preliminary results which suggest that some field theory models are `almost` integrable; i.e. they possess a large number of `almost` conserved quantities. First we demonstrate this, in some detail, on a class of models which generalise sine-Gordon model in (1+1) dimensions. Then, we point out that many field configurations of these models look like those of the integrable systems and others are very close to being integrable. Finally we attempt to quantify these claims looking in particular, both analytically and numerically, at some long lived field configurations which resemble breathers.

Axially symmetric soliton solutions in a Skyrme-Faddeev-type model with Gies`s extension

We construct static soliton solutions with non-zero Hopf topological charges to a theory which is the extended Skyrme-Faddeev model with a further quartic term in derivatives. We use an axially symmetric ansatz based on toroidal coordinates, and solve the resulting two coupled nonlinear partial differential equations in two variables by a successive over-relaxation method. We construct numerical solutions with the Hopf charge up to 4. The solutions present an interesting behavior under the changes of a special combination of the coupling constants of the quartic terms.

Exact vortex solutions in a CP(N) Skyrme-Faddeev type model

We consider a four dimensional field theory with target space being CP(N) which constitutes a generalization of the usual Skyrme-Faddeev model defined on CP(1). We show that it possesses an integrable sector presenting an infinite number of local conservation laws, which are associated to the hidden symmetries of the zero curvature representation of the theory in loop space. We construct an infinite class of exact solutions for that integrable submodel where the fields are meromorphic functions of the combinations (x(1) + i x(2)) and (x(3) + x(0)) of the Cartesian coordinates of four dimensional Minkowski space-time. Among those solutions we have static vortices and also vortices with waves traveling along them with the speed of light. The energy per unity of length of the vortices show an interesting and intricate interaction among the vortices and waves.

Thermal lens spectrometry in pyroelectric lithium niobate crystals

In this work, the light-induced lens effect due to thermal and/or photorefractive processes was studied in pyroelectric (undoped and Fe(2+)-doped) lithium niobate crystals (LiNbO(3)) using thermal lens spectrometry with a two-beam (pump-probe) mode-mismatched configuration. The measurements were carried out at two pump beam wavelengths (514.5 and 750 nm) to establish a full understanding of the present effects in this material (thermal and/or photorefractive). We present an easy-to-implement method to determine quantitative values of the pyroelectric coefficient (dPs/dT), its contribution to the thermal effect and other thermo-optical parameters like thermal diffusivity (D), thermal conductivity (K) and temperature coefficient of the optical path length change (ds/dT). These measurements were performed in LiNbO(3) and LiNbO(3): Fe (0.1 ppm Fe(2+)) crystals with c axis along the direction of laser propagation.

Novo sistema de aplicação de drogas em cirurgias oftalmológicas

The topical corneal application of antimitotic mitomycin-C (MMC) during refractive surgery is still characterized by a lack of standardization and considerable empirism. For this reason the creation of a system capable of reliable drug delivery represents a beneficial innovation for patients submitted to these procedures. Objective: Elaborate a new MMC delivery system during the transoperatory period of photorefractive keratectomy (PRK) followed by patent application. Methods: The project consists of an in vitro experimental study to create an MMC (0.02%) release system. The drug was impregnated in sterile Whatman® 41 paper filter discs with a diameter of 8 mm. After drying, the discs were applied to antibiogram plates seeded with Staphylococcus epidermidis (American Type Culture Collection ATCC 12228), followed by the addition of a drop of sterile water. At the end of 1 minute, the discs were removed and the plates incubated for 48 hours at 35oC. Mean drop volume in the collyrium flasks was measured using analytical balance weighing. The inhibition halo (mm) was correlated with the MMC impregnated into the disc. After completion of the invention design a patent application was lodged at the National Institute of Industrial Property. Results: The correspondence between MMC-produced inhibition halos indicated that a dose of 16μg was ideal for impregnating into the discs. The mean drop volume obtained from the collyrium flasks was 37.7 μL. A minute after the application of one drop of balanced saline solution, the system released an adequate concentration for PRK surgery. Conclusion: A new MMC delivery system was created for transoperatory application in photorefractive keratectomy (PRK). Publication of the patent application (number PI 0704739-8) gives the authors exclusive intellectual property rights. The study was sponsored by Ophthalmos Indústria e Comércio de Produtos Farmacêuticos S.A. (São Paulo-SP, Brazil) and received the indispensable scientific contribution of researchers from the fields of Pharmacy, Medicine, Biology, Statistics and Law, characterizing the work as multidisciplinary, in accordance with norms established by the Postgraduate Health Sciences Program of the Federal University of Rio Grande do Norte (UFRN)

Bifurcation analysis of a new Lorenz-like chaotic system

In this paper we study the local codimension one and two bifurcations which occur in a family of three-dimensional vector fields depending on three parameters. An equivalent family, depending on five parameters, was recently proposed as a new chaotic system with a Lorenz-like butterfly shaped attractor and was studied mainly from a numerical point of view, for particular values of the parameters, for which computational evidences of the chaotic attractor was shown. In order to contribute to the understand of this new system we present an analytical study and the bifurcation diagrams of an equivalent three parameter system, showing the qualitative changes in the dynamics of its solutions, for different values of the parameters. (C) 2007 Elsevier Ltd. All rights reserved.

Fermions bounded by kinks of false vacuum models

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Continuously deformable topological structure

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On turbulent, erratic and other dynamical properties of Zadeh's extensions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dynamics at infinity and other global dynamical aspects of Shimizu-Morioka equations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On asymptotic solutions of integrable wave equations

Asymptotic 'soliton train' solutions of integrable wave equations described by inverse scattering transform method with second-order scalar eigenvalue problem are considered. It is shown that if asymptotic solution can be presented as a modulated one-phase nonlinear periodic wavetrain, then the corresponding Baker-Akhiezer function transforms into quasiclassical eigenfunction of the linear spectral problem in weak dispersion limit for initially smooth pulses. In this quasiclassical limit the corresponding eigenvalues can be calculated with the use of the Bohr Sommerfeld quantization rule. The asymptotic distributions of solitons parameters obtained in this way specify the solution of the Whitham equations. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms

We consider formation of dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms. It is shown that for big enough initial inhomogeneity of density, interplay of nonlinear and dispersion effects leads to wave breaking phenomenon followed by generation of a train of dark solitons. Analytical theory is confirmed by numerical simulations.

Stabilization of a (3+1)-dimensional soliton in a Kerr medium by a rapidly oscillating dispersion coefficient

Using the numerical solution of the nonlinear Schrodinger equation and a variational method it is shown that (3 + 1)-dimensional spatiotemporal optical solitons can be stabilized by a rapidly oscillating dispersion coefficient in a Kerr medium with cubic nonlinearity. This has immediate consequence in generating dispersion-managed robust optical soliton in communication as well as possible stabilized Bose-Einstein condensates in periodic optical-lattice potential via an effective-mass formulation. We also critically compare the present stabilization with that obtained by a rapid sinusoidal oscillation of the Kerr nonlinearity parameter.

Infrared degrees of freedom of Yang-Mills theory in the Schrodinger representation

We set up a new calculational framework for the Yang-Mills vacuum transition amplitude in the Schrodinger representation. After integrating out hard-mode contributions perturbatively and performing a gauge-invariant gradient expansion of the ensuing soft-mode action, a manageable saddle-point expansion for the vacuum overlap can be formulated. In combination with the squeezed approximation to the vacuum wave functional this allows for an essentially analytical treatment of physical amplitudes. Moreover, it leads to the identification of dominant and gauge-invariant classes of gauge field orbits which play the role of gluonic infrared (IR) degrees of freedom. The latter emerge as a diverse set of saddle-point solutions and are represented by unitary matrix fields. We discuss their scale stability, the associated virial theorem and other general properties including topological quantum numbers and action bounds. We then find important saddle-point solutions (most of them solitons) explicitly and examine their physical impact. While some are related to tunneling solutions of the classical Yang-Mills equation, i.e. to instantons and merons, others appear to play unprecedented roles. A remarkable new class of IR degrees of freedom consists of Faddeev-Niemi type link and knot solutions, potentially related to glueballs.