Leadership Cartels in Industries with Differentiated Products.

This article analyses cartels that act as a Stackelberg leader with respect to a competitive fringe in industries supplying differentiated products. The main objectives are to investigate how cartel stability changes with the degree of differentiation and the cartel size, to predict endogenous cartels and to carry out a welfare analysis. Both repeated and static games are considered as well as industries competing in quantities and prices.CARTELS ; GAMES ; COMPETITION ; SIZE OF INDUSTRY

Simple quantum password checking

We present a quantum password checking protocol where secrecy is protected by the laws of quantum mechanics. The passwords are encoded in quantum systems that can be compared but have a dimension too small to allow reading the encoded bits. We study the protocol under different replay attacks and show it is robust even for poorly chosen passwords.Comment: 5 pages. Comments welcom

Helmholtz-Manakov solitons

A novel spatial soliton-bearing wave equation is introduced, the Helmholtz-Manakov (H-M) equation, for describing the evolution of broad multi-component self-trapped beams in Kerr-type media. By omitting the slowly-varying envelope approximation, the H-M equation can describe accurately vector solitons propagating and interacting at arbitrarily large angles with respect to the reference direction. The H-M equation is solved using Hirota’s method, yielding four new classes of Helmholtz soliton that are vector generalizations of their scalar counterparts. General and particular forms of the three invariants of the H-M system are also reported

Propagation properties of nonparaxial spatial solitons

We present an analysis and simulation of the non-paraxial nonlinear Schroedinger equation. Exact general relations describing energy flow conservation and transformation invariance are reported, and then explained on physical grounds. New instabilities of fundamental and higher-order paraxial solitons are discovered in regimes where exact analytical non-paraxial solitons are found to be robust attractors. Inverse-scattering theory and the known form of solutions are shown to enable the prediction of the characteristics of nonparaxial soliton formation. Finally, analysis of higher-order soliton break up due to non-paraxial effects reveals features that appear to be of a rather general nature

Bistable dark solitons of a cubic-quintic Helmholtz equation

We report, to the best of our knowledge, the first exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field, and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and non-degenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit. We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors