Dynamics of Lattice Kinks

In this paper we consider two models of soliton dynamics (the sine Gordon and the \phi^4 equations) on a 1-dimensional lattice. We are interested in particular in the behavior of their kink-like solutions inside the Peierls- Nabarro barrier and its variation as a function of the discreteness parameter. We find explicitly the asymptotic states of the system for any value of the discreteness parameter and the rates of decay of the initial data to these asymptotic states. We show that genuinely periodic solutions are possible and we identify the regimes of the discreteness parameter for which they are expected to persist. We also prove that quasiperiodic solutions cannot exist. Our results are verified by numerical simulations.Comment: 50 pages, 10 figures, LaTeX documen

Stability criterion for bright solitary waves of the perturbed cubic-quintic Schroedinger equation

The stability of the bright solitary wave solution to the perturbed cubic-quintic Schroedinger equation is considered. It is shown that in a certain region of parameter space these solutions are unstable, with the instability being manifested as a small positive eigenvalue. Furthermore, it is shown that in the complimentary region of parameter space there are no small unstable eigenvalues. The proof involves a novel calculation of the Evans function, which is of interest in its own right. As a consequence of the eigenvalue calculation, it is additionally shown that N-bump bright solitary waves bifurcate from the primary wave.Comment: 28 pages, LaTeX, submitted; author info at http://www.math.unm.edu/~kapitul

The Ethical Triage and Management Guidelines of the Entrapped and Mangled Extremity in Resource Scarce Environments: A Systematic Literature Review.

ABSTRACTObjective:A systematic literature review (SLR) was performed to elucidate the current triage and treatment of an entrapped or mangled extremity in resource scarce environments (RSEs).Methods:A lead researcher followed the search strategy following inclusion and exclusion criteria. A first reviewer (FR) was randomly assigned sources. One of the 2 lead researchers was the second reviewer (SR). Each determined the level of evidence (LOE) and quality of evidence (QE) from each source. Any differing opinions between the FR and SR were discussed between them, and if differing opinions remained, then a third reviewer (the other lead researcher) discussed the article until a consensus was reached. The final opinion of each article was entered for analysis.Results:Fifty-eight (58) articles were entered into the final study. There was 1 study determined to be LOE 1, 29 LOE 2, and 28 LOE 3, with 15 determined to achieve QE 1, 37 QE 2, and 6 QE 3.Conclusion:This SLR showed that there is a lack of studies producing strong evidence to support the triage and treatment of the mangled extremity in RSE. Therefore, a Delphi process is suggested to adapt and modify current civilian and military triage and treatment guidelines to the RSE