Legendre transformations on the triangular lattice

The main purpose of the paper is to demonstrate that condition of invariance with respect to the Legendre transformations allows effectively isolate the class of integrable difference equations on the triangular lattice, which can be considered as discrete analogues of relativistic Toda type lattices. Some of obtained equations are new, up to the author knowledge. As an example, one of them is studied in more details, in particular, its higher continuous symmetries and zero curvature representation are found.Comment: 13 pages, late

Competitive localization of vortex lines and interacting bosons

We present a theory for the localization of three-dimensional vortex lines or two-dimensional bosons with short-ranged repulsive interaction which are competing for a single columnar defect or potential well. For two vortices we use a necklace model approach to find a new kind of delocalization transition between two different states with a single bound particle. This exchange-delocalization transition is characterized by the onset of vortex exchange on the defect for sufficiently weak vortex-vortex repulsion or sufficiently weak binding energy corresponding to high temperature. We calculate the transition point and order of the exchange-delocalization transition. A generalization of this transition to arbitrary vortex number is proposed.Comment: 5 pages, 2 figure

On the structure of the B\"acklund transformations for the relativistic lattices

The B\"acklund transformations for the relativistic lattices of the Toda type and their discrete analogues can be obtained as the composition of two duality transformations. The condition of invariance under this composition allows to distinguish effectively the integrable cases. Iterations of the B\"acklund transformations can be described in the terms of nonrelativistic lattices of the Toda type. Several multifield generalizations are presented

A note on the integrable discretization of the nonlinear Schr\"odinger equation

We revisit integrable discretizations for the nonlinear Schr\"odinger equation due to Ablowitz and Ladik. We demonstrate how their main drawback, the non-locality, can be overcome. Namely, we factorize the non-local difference scheme into the product of local ones. This must improve the performance of the scheme in the numerical computations dramatically. Using the equivalence of the Ablowitz--Ladik and the relativistic Toda hierarchies, we find the interpolating Hamiltonians for the local schemes and show how to solve them in terms of matrix factorizations.Comment: 24 pages, LaTeX, revised and extended versio

Tobacco and cannabis use trajectories from adolescence to young adulthood

The main objective of this longitudinal research is to answer the following question: What is the relationship between tobacco and cannabis use trajectories from adolescence to young adulthood? And more specifically we are interested in: A. If the use of one of the substances (tobacco or cannabis) decreases overtime, does the use of the other one increase to compensate? Are other substances (such as alcohol, for example) also used to compensate in these cases? B. Does the probability to become a tobacco smoker increase when cannabis use is heavier or has lasted longer? C. What are the risk and protective factors that can predict that the use of tobacco and/or cannabis will increase or decrease overtime

Room-temperature transverse-electric polarized intersubband electroluminescence from InAs/AlInAs quantum dashes

We report the observation of transverse electric polarized electroluminescence from InAs/AlInAs quantum dash quantum cascade structures up to room temperature. The emission is attributed to the electric field confined along the shortest lateral dimension of the dashes, as confirmed by its dependence on crystallographic orientation both in absorption measurements on a dedicated sample and from electroluminescence itself. From the absorption we estimate a dipole moment for the observed transition of =1.7 nm. The electroluminescence is peaked at around 110 meV and increases with applied bias. Its temperature dependence shows a decrease at higher temperatures limited by optical phonon emission.Comment: 15 pages, 4 figures, submitted to Applied Physics Letter

On the Lagrangian structure of integrable hierarchies

We develop the concept of pluri-Lagrangian structures for integrable hierarchies. This is a continuous counterpart of the pluri-Lagrangian (or Lagrangian multiform) theory of integrable lattice systems. We derive the multi-time Euler Lagrange equations in their full generality for hierarchies of two-dimensional systems, and construct a pluri-Lagrangian formulation of the potential Korteweg-de Vries hierarchy.Comment: 29 page