Group-invariant solutions of semilinear Schrodinger equations in multi-dimensions

Symmetry group methods are applied to obtain all explicit group-invariant radial solutions to a class of semilinear Schr¨odinger equations in dimensions n = 1. Both focusing and defocusing cases of a power nonlinearity are considered, including the special case of the pseudo-conformal power p = 4/n relevant for critical dynamics. The methods involve, first, reduction of the Schr¨odinger equations to group-invariant semilinear complex 2nd order ordinary differential equations (ODEs) with respect to an optimal set of one-dimensional point symmetry groups, and second, use of inherited symmetries, hidden symmetries, and conditional symmetries to solve each ODE by quadratures. Through Noether’s theorem, all conservation laws arising from these point symmetry groups are listed. Some group-invariant solutions are found to exist for values of n other than just positive integers, and in such cases an alternative two-dimensional form of the Schr¨odinger equations involving an extra modulation term with a parameter m = 2−n = 0 is discussed.

BP BLOGGER: DESCRIPTIVE STUDY OF ELECTRONIC KNOWLEDGE DISSEMINATION IN LONG TERM CARE

Little is known of the uptake and use of knowledge disseminated in electronic formats, especially in Long Term Care (LTC) settings. The purpose of this descriptive study was to examine the dissemination of the BP Bloggers, a series of brief, evidence summaries designed to meet the knowledge needs of LTC staff. Guided by Rogers’ (2003) Diffusion of Innovations theory, the study documents dissemination of the BP Blogger and examines factors affecting dissemination, awareness, perceptions and its use. The survey of BP Blogger recipients was conducted electronically (n=114) online (n=10), by telephone (n=55), and print (n=144). Managers usually received the newsletter electronically while staff in LTC were more likely to receive printed copies. Participants disseminated the newsletter through paper, email, or posting in the workplace. Most participants rated the content, format, and usefulness of the BP Blogger as good or excellent. Time and lack of email access were barriers to dissemination.