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 sl(N) constrained KP hierarchy and giving rise to the negative Borel sl(N) loop algebra is indicated.Comment: 8 pages, LaTeX, typos corrected, references update

The experiences of patients and carers in the daily management of care at the end of life

Background Home is the preferred location for most people with an advanced disease and at the end of life. A variety of care professionals work in community settings to provide support to this population. Patients and their spouses, who also care for them (spouse-carers), are rarely accompanied by these sources of support at all times, and have to manage independently between their contact with care professionals. Aim To explore how patients and spouse-carers manage their involvement with care professionals in the community setting. Method Interpretive phenomenology informs the design of the research, whereby 16 interviews were conducted with the patients and spouse-carers. Interviews were recorded and transcribed verbatim. Data were analysed using phenomenological techniques including template analysis. Findings Patients and spouse-carers were interdependent and both parties played a role in co-ordinating care and managing relationships with professional care providers. The patients and spouse-carers actively made choices about how to manage their situation, and develop and modify managing strategies based on their experiences. Conclusions When daily management is effective and care professionals acknowledge the dyadic nature of the patient and spouse-carer relationship, people have confidence in living with advanced disease

Supersymmetry for integrable hierarchies on loop superalgebras

The algebraic approach is employed to formulate N=2 supersymmetry transformations in the context of integrable systems based on loop superalgebras $\hat{\rm sl}(p+1,p), p \ge 1$ with homogeneous gradation. We work with extended integrable hierarchies, which contain supersymmetric AKNS and Lund-Regge sectors. We derive the one-soliton solution for $p=1$ which solves positive and negative evolution equations of the N=2 supersymmetric model.Comment: Latex, 21 page