Permutability of Backlund transformation for N=1 supersymmetric sinh-Gordon

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Backlund transformation for integrable hierarchies: example - mKdV hierarchy

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model

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

Type-II Backlund transformations via gauge transformations

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

Exact-Solutions Of Linear Partial-Differential Equations With Variable-Coefficients

Backlund transformations relating the solutions of linear PDE with variable coefficients to those of PDE with constant coefficients are found, generalizing the study of Varley and Seymour [2]. Auto-Backlund transformations are also determined. To facilitate the generation of new solutions via Backlund transformation, explicit solutions of both classes of the PDE just mentioned are found using invariance properties of these equations and other methods. Some of these solutions are new.

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.

The higher grading structure of the WKI hierarchy and the two-component short pulse equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Integrablility of a classical N=2 super sinh-Gordon model with jump defects

The Lagrangian formalism for the N = 2 supersymmetric sinh-Gordon model with a jump defect is considered. The modified conserved momentum and energy are constructed in terms of border functions. The supersymmetric Backlund transformation is given and an one-soliton solution is obtained.The Lax formulation based on the affine super Lie algebra sl(2, 2) within the space split by the defect leads to the integrability of the model and henceforth to the existence of an infinite number of constants of motion.

Grassmannian and bosonic Thirring models with jump defects

In this paper we discuss the Lax formulation of the Grassmannian and Bosonic Thirring models in the presence of jump defects. For the Grassmannian case, the defect is described by Backlund transformation which is responsible for preserving the integrability of the model. We then propose an extension of the Backlund transformation for the Bosonic Thirring model which is verified by some Backlund transitions like vacuum-one soliton, one soliton-one soliton, one soliton-two solitons and two solitons-two solitons. The Lax formulation within the space split by the defect leads to the integrability of Bosonic Thirring model with jump defects.

Type-II defects in the super-Liouville theory

The introduction of type-II defects is discussed under the Lagrangian formalism and Lax representation for the N = 1 super-Liouville model. We derive a new kind of super-Backlund transformation for the model and show explicitly the conservation of the modified energy and momentum, as well as supercharge.

O modelo de Schrödinger não linear com um defeito integrável

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Backlund-Darboux Transformations in Sato's Grassmannian

We define Bäcklund–Darboux transformations in Sato’s Grassmannian. They can be regarded as Darboux transformations on maximal algebras of commuting ordinary differential operators. We describe the action of these transformations on related objects: wave functions, tau-functions and spectral algebras.

Extreme Sports: A positive transformation in courage and humility

Extreme sports and extreme sports participants have been most commonly explored from a negative perspective, for example the “need to take unnecessary risks.” This study explored what can be learned from extreme sports about courage and humility - two positive psychology constructs. A phenomenological method was used via unstructured interviews with 15 extreme sports participants and other first hand accounts. The extreme sports included B.A.S.E. jumping, big wave surfing, extreme skiing, waterfall kayaking, extreme mountaineering and solo rope-free climbing. Results indicate that humility and courage can be deliberately sought out by participating in activities that involve a real chance of death, fear and the realisation that nature in its extreme is far greater and more powerful than humanity.

Creative industries in China : four perspectives on social transformation

In late 2004, the concept of the creative industries arrived in China. It was warmly welcomed in Shanghai then subsequently adopted with some degree of caution in Beijing. In the years since, officials, scholars, practitioners, entrepreneurs and developers have exploited of the idea of creative industries, and a range of associated terms, to construct an alternative vision of an emerging China. In 2009, Li Wuwei, the Director of the Shanghai Creative Industries Association, himself a leading player in national political reform, released a book titled Creativity is Changing China (Chuangyi gaibian Zhongguo), subsequently translated as Creative Industries Are Changing China in English. The paper investigates the uptake of the creative industries in China and asks: can they really change China, or are they just rearranging the cultural landscape in some cities?