Unheard voices: A qualitative study of LGBT+ older people experiences during the first wave of the COVID-19 pandemic in the UK

This paper reports findings from a qualitative study into the immediate impact of social distancing measures on the lives of lesbian, gay, bisexual and trans (LGBT+) older people (≥60 years) living in the UK during the first lockdown of the COVID-19 pandemic. It draws on in-depth interviews with 17 older people and 6 key informants from LGBT+ community-based organisations, exploring the strategies used to manage their situations, how they responded and adapted to key challenges. Five themes emerged related to: 1) risk factors for LGBT+ older people and organisations, including specific findings on trans experiences,;2) care practices in LGBT+ lives,;3) strengths and benefits of networking 4) politicisation of ageing issues and their relevance to LGBT+ communities; and 5) learning from communication and provision in a virtual world. The findings illuminate adaptability and many strengths in relation to affective equality and reciprocal love, care and support among LGBT+ older people. It is vital UK that the government recognises and addresses the needs and concerns of LGBT+ older people during emergencies. What is known: The coronavirus (COVID-19) pandemic, and the wider governmental and societal response, brought health inequalities into sharp focus, exposing the structural disadvantage and discrimination faced by many marginalised communities in the UK and globally. LGBT+ older people are known to experience health inequalities compounded by anticipated or poor experiences of accessing health and social care services. What this paper adds: An exploration of LGBT+ older peple, their communities and social networks and how these were adapted in the COVID-19 context. Trans older people have been affected in very specific ways. The findings illuminate adaptability and many strengths in relation to affective equality and reciprocal love, care and support among LGBT+ older people. It is vital UK that the government recognises and addresses the needs and concerns of LGBT+ older people during emergencies

Multiscale analysis of discrete nonlinear evolution equations: The reduction of the dNLS

In this paper we consider multiple lattices and functions defined on them. We introduce some slow varying conditions and define a multiscale analysis on the lattice, i.e. a way to express the variation of a function in one lattice in terms of an asymptotic expansion with respect to the other. We apply these results to the case of the multiscale expansion of the differential-difference Nonlinear Schrodinger equation

The discrete nonlinear Schrodinger equation and its lie symmetry reductions

The Lie algebra L(h) of symmetries of a discrete analogue of the non-linear Schrodinger equation (NLS) is studied. A five-dimensional subspace of L(h), generated by both point and generalized symmetries, transforms into the five-dimensional point symmetry algebra L(0) of the NLS equation. We use the lowest symmetries to do symmetry reduction of the equation, thus obtaining explicit solutions and discrete analogues of elliptic functions

Symmetries of the discrete nonlinear Schrodinger equation

The Lie algebra L(h) of point symmetries of a discrete analogue of the nonlinear Schrodinger equation (NLS) is described. In the continuous limit, the discrete equation is transformed into the NLS, while the structure of the Lie algebra changes: a contraction occurs with the lattice spacing h as the contraction parameter. A live-dimensional subspace of L(h), generated by both point and generalized symmetries, transforms into the hire-dimensional point symmetry algebra of the NLS

Symmetries of the discrete Burgers equation

A discrete Cole-Hopf transformation is used to derive a discrete Burgers equation that is linearizable to a discrete heat equation. A five-dimensional symmetry algebra is obtained that reduces to the Lie point symmetry algebra of the usual Burgers equation, in the continuous limit. This Lie algebra is used to obtain explicit invariant solutions

Lie algebra contractions and symmetries of the Toda hierarchy

The Lie algebra L(Delta) of generalized and point symmetries of the equations in the Toda hierarchy is shown to be a semidirect sum of two infinite-dimensional Lie algebras, one perfect, the other Abelian. In the continuous limit the structure of the Lie algebra changes: a contraction occurs with the lattice spacing as the contraction parameter. In particular, for the Toda equation itself, a set of five elements, involving both point symmetries and generalized ones, contracts to the point symmetry algebra of the potential KdV equation

Relation between Backlund transformations and higher continuous symmetries of the Toda equation

In this paper we study one aspect of the continuous symmetries of the Toda equation. Namely, we establish a correspondence between Backlund transformations and continuous symmetries of the Toda equation. A symmetry transformation acting on a solution of the Toda equation can be seen as a superposition of Backlund transformations. Conversely, a Backlund transformation can be written, at least formally, as a composition of infinitely many higher symmetry transformations. This result reinforces the opinion that the presence of sufficiently many continuous symmetries for discrete equations is an indication of their integrability

Multiscale expansion on the lattice and integrability of partial difference equations

We conjecture an integrability and linearizability test for dispersive Z(2)-lattice equations by using a discrete multiscale analysis. The lowest order secularity conditions from the multiscale expansion give a partial differential equation of the form of a nonlinear Schrodinger (NLS) equation. If the starting lattice equation is integrable then the resulting NLS-type equation turns out to be integrable, while if the starting equation is linearizable we get a linear Schrodinger equation. On the other hand, if we start with a non-integrable lattice equation the resulting equation can be both integrable and non-integrable. This conjecture is confirmed by many examples

Multiscale expansion of the lattice potential KdV equation on functions of an infinite slow-varyness order

We present a discrete multiscale expansion of the lattice potential Korteweg-de Vries (lpKdV) equation on functions of an infinite order of slow varyness. To do so, we introduce a formal expansion of the shift operator on many lattices holding at all orders. The lowest secularity condition from the expansion of the lpKdV equation gives a nonlinear lattice equation, depending on shifts of all orders, of the form of the nonlinear Schrodinger equation