The concept of quasi-integrability for modified non-linear Schrodinger models

We consider modifications of the nonlinear Schrodinger model (NLS) to look at the recently introduced concept of quasi-integrability. We show that such models possess an in finite number of quasi-conserved charges which present intriguing properties in relation to very specific space-time parity transformations. For the case of two-soliton solutions where the fields are eigenstates of this parity, those charges are asymptotically conserved in the scattering process of the solitons. Even though the charges vary in time their values in the far past and the far future are the same. Such results are obtained through analytical and numerical methods, and employ adaptations of algebraic techniques used in integrable field theories. Our findings may have important consequences on the applications of these models in several areas of non-linear science. We make a detailed numerical study of the modified NLS potential of the form V similar to (vertical bar psi vertical bar(2))(2+epsilon), with epsilon being a perturbation parameter. We perform numerical simulations of the scattering of solitons for this model and find a good agreement with the results predicted by the analytical considerations. Our paper shows that the quasi-integrability concepts recently proposed in the context of modifications of the sine-Gordon model remain valid for perturbations of the NLS model.

ATTEMPTS TO DEFINE QUASI-INTEGRABILITY

In this paper we discuss some ideas on how to define the concept of quasi-integrability. Our ideas stem from the observation that many field theory models are "almost" integrable; i.e. they possess a large number of "almost" conserved quantities. Most of our discussion will involve a certain class of models which generalize the sine-Gordon model in (1 + 1) dimensions. As will be mentioned many field configurations of these models look like those of the integrable systems and so appear to be close to those in integrable model. We will then attempt to quantify these claims looking in particular, both analytically and numerically, at field configurations with scattering solitons. We will also discuss some preliminary results obtained in other models.

Systemic sclerosis sine scleroderma associated with antiphospholipid syndrome

The antiphospholipid syndrome (APS) can be primary, when it occurs alone, or secondary, when it is associated with another autoimmune disease, mainly systemic lupus erythematosus and rarely other autoimmune diseases. Cases described in literature (Medline 1966 to December 2009) associate the presence of antiphospholipid antibodies with the presence of APS and systemic sclerosis (SS). Currently, however, no cases of the SS variant sine scleroderma with APS have been described. In this study, the authors describe the case of a patient with APS characterised by thrombosis of the retinal veins, in May 2006, the presence of lupus anticoagulant and an anticardiolipin IgG antibody. In May 2007, this patient developed Raynaud's phenomenon, a lack of oesophageal motility and nailfold capillaroscopy with a scleroderma pattern. The patient was positive for the anti-centromere antibody but lacked any evidence of cutaneous thickening or involvement. In summary, the authors describe the first case of a patient with APS associated with SS sine scleroderma.