Estrutura algébrica de hierarquias integráveis e problemas de valor de contorno

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Supersymmetry of Affine Toda Models as Fermionic Symmetry Flows of the Extended mKdV Hierarchy

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

Backlund transformation for integrable hierarchies: example - mKdV hierarchy

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Supersymmetry and the KdV equations for integrable hierarchies with a half-integer gradation

Supersymmetry is formulated for integrable models based on the sl(2 1) loop algebra endowed with a principal gradation. The symmetry transformations which have half-integer grades generate supersymmetry. The sl(2 1) loop algebra leads to N=2 supersymmetric mKdV and sinh-Gordon equations. The corresponding N=1 mKdV and sinh-Gordon equations are obtained via reduction induced by twisted automorphism. Our method allows for a description of a non-local symmetry structure of supersymmetric integrable models. © 2003 Elsevier B.V. All rights reserved.

Integrable field theories with defects

The structure of integrable field theories in the presence of defects is discussed in terms of boundary functions under the Lagrangian formalism. Explicit examples of bosonic and fermionic theories are considered. In particular, the boundary functions for the super sinh-Gordon model is constructed and shown to generate the Backlund transformations for its soliton solutions.

Noncommutative integrable field theories in 2d

We study the noncommutative generalization of (Euclidean) integrable models in two dimensions, specifically the sine- and sinh-Gordon and the U(N) principal chiral models. By looking at tree-level amplitudes for the sinh-Gordon model we show that its naive noncommutative generalization is not integrable. on the other hand, the addition of extra constraints, obtained through the generalization of the zero-curvature method, renders the model integrable. We construct explicit nonlocal nontrivial conserved charges for the U(N) principal chiral model using the Brezin-Itzykson-Zinn-Justin-Zuber method. (C) 2003 Elsevier B.V. All rights reserved.

Construction of exact Riemannian instanton solutions

We present the exact construction of Riemannian (or stringy) instantons, which are classical solutions of 2D Yang-Mills theories that interpolate between initial and final string configurations. They satisfy the Hitchin equations with special boundary conditions. For the case of U(2) gauge group those equations can be written as the sinh-Gordon equation with a delta-function source. Using the techniques of integrable theories based on the zero curvature conditions, we show that the solution is a condensate of an infinite number of one-solitons with the same topological charge and with all possible rapidities.

Modelos integráveis multicarregados e integrabilidade no plano não comutativo

Pós-graduação em Física - IFT

The complex sine-Gordon equation as a symmetry flow of the AKNS hierarchy

It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the 'negative' symmetry flows forming the Borel loop algebra. The complex sine-Gordon and the vector nonlinear Schrodinger equations appear as lowest-negative and second-positive flows within the extended hierarchy. This is fully analogous to the well known connection between the sine-Gordon and mKdV equations within the extended mKdV hierarchy. A general formalism for a Toda-like symmetry occupying the 'negative' sector of the sl(N) constrained KP hierarchy and giving rise to the negative Borel sl(N) loop algebra is indicated.

Book Review : Beyond criminology : taking harm seriously edited by Paddy Hillyard, Christina Pantazis, Steve Tombs and Dave Gordon (2004)

Hillyard et al.'s Beyond Criminology: Taking Crime Seriously is an innovative collection that attempts to take criminology beyond state definitions of crime to discourses involving harm, or what the editors refer to as ‘zemiology’, or what could be called ‘social harm theory’. The central theme of the book is that ‘it makes no sense to separate out harms, which can be defined as criminal, from all other types of harm’ (p. 2). At long last, ‘harm’ is discussed with the theoretical and practical integrity it deserves as an academic and intellectual narrative. For too long it has been ignored or omitted from the criminological lexicon. This book ensures that it captures centre stage within analyses that refocus the agenda to deleterious acts not always covered by the state legislature...

How Gordon Ramsay appeals to consumers : effects of self-concept clarity and celebrity meaning on celebrity endorsements

How do celebrities like Gordon Ramsay appeal to consumers? This article examines one explanation. We study how celebrities appeal to consumers in the context of celebrity chefs. We examine how a consumer's self-concept clarity (SCC) interacts with their perception of the meaning that a celebrity endorser possesses. An experiment comparing fictional ads endorsed by different celebrity chefs yields the surprising result that consumers with a clear sense of who they are (high-SCC consumers) are more influenced by an ad featuring a celebrity high in meaning (Ramsay), whereas low-SCC consumers are influenced to slightly higher levels by a celebrity with lower levels of celebrity meaning.

A family of interesting exact solutions of the sine-Gordon equation

By using AKNS [Phys. Rev. Lett. 31 (1973) 125] system and introducing the wave function, a family of interesting exact solutions of the sine-Gordon equation are constructed. These solutions seem to be some soliton, kink, and anti-kink ones respectively for the different choice of the spectrum, whereas due to the interaction between two traveling-waves they have some properties different from usual soliton, kink, and anti-kink solutions.

A new method of studying the dynamical behavior of the sine-gordon equation

We try to connect the theory of infinite dimensional dynamical systems and nonlinear dynamical methods. The sine-Gordon equation is used to illustrate our method of discussing the dynamical behaviour of infinite dimensional systems. The results agree with those of Bishop and Flesch [SLAM J. Math. Anal. 21 (1990) 1511].

Sine-Gordon方程的截断系统的同宿轨道

研究ＳｉｎｅＧｏｒｄｏｎ方程的广义渐近惯性流形上的常微分方程组，证实了在一定参数条件下存在Ｗｉｇｇｉｎｓ［１］意义下的同宿轨道．计算表明，与Ｂｉｓｈｏｐ［２］用数值计算得到的ＳｉｎｅＧｏｒｄｏｎ方程产生混沌的参数值尚有差别，考虑到同宿出现参数值往往低于混沌出现参数值，故结果在定性上正确，而且改进了文［１］中的结果．