Conditional Symmetries and Riemann Invariants for Hyperbolic Systems of PDEs

This paper contains an analysis of rank-k solutions in terms of Riemann invariants, obtained from interrelations between two concepts, that of the symmetry reduction method and of the generalized method of characteristics for first order quasilinear hyperbolic systems of PDEs in many dimensions. A variant of the conditional symmetry method for obtaining this type of solutions is proposed. A Lie module of vector fields, which are symmetries of an overdetermined system defined by the initial system of equations and certain first order differential constraints, is constructed. It is shown that this overdetermined system admits rank-k solutions expressible in terms of Riemann invariants. Finally, examples of applications of the proposed approach to the fluid dynamics equations in (k+1) dimensions are discussed in detail. Several new soliton-like solutions (among them kinks, bumps and multiple wave solutions) have been obtained

Elliptic solutions of isentropic ideal compressible fluid flow in (3 + 1) dimensions

A modified version of the conditional symmetry method, together with the classical method, is used to obtain new classes of elliptic solutions of the isentropic ideal compressible fluid flow in (3+1) dimensions. We focus on those types of solutions which are expressed in terms of the Weierstrass P-functions of Riemann invariants. These solutions are of special interest since we show that they remain bounded even when these invariants admit the gradient catastrophe. We describe in detail a procedure for constructing such classes of solutions. Finally, we present several examples of an application of our approach which includes bumps, kinks and multi-wave solutions

Utilisation durable de l'eau, des zones humides et de la diversité biologique dans les éco-systèmes partagés : Bénin, Burkina Faso, Niger, Togo

Le fait pastoral dans la région du parc du "W" du Niger est analysé dans le but de détacher une politique de gestion des parcours en périphérie. Un dialogue entre les responsables de la conservation et les éleveurs à ce propos ne paraît possible que si le parc est admis par tous et dûment contrôlé. (Résumé d'auteur

Une philosophie pour le parc national du Niokolo-Koba et sa région (Sénégal) : réhabilitation de l'aire protégée et éco-gestion de sa périphérie

Le Parc National du Niokolo Koba (Sénégal) est actuellement dans une situation délicate. Sa richesse biologique encore réelle est en sursis. Un budget dérisoire et l'absence d'investissement depuis des années font que les acquis ne sont plus maintenus. Pendant ce temps, les populations voisines sacrifient à la culture minière du coton. Elles n'en négligent pas pour autant l'usage des ressources animales et végétales qui constituent pour elles la vrai richesse et qui ne se trouvent plus guère que dans le parc, surtout la grand faune. Il est urgent d'élaborer un plan de réhabilitation de l'aire protégée et de définir une politique pour sa périphérie. Celle-ci devra être conçue en accord avec l'éthos des communautés humaines voisines. (Résumé d'auteur

A world without farmers? Food production, inclusive development and ecology: Historical Evidences for a New Deal

This paper questions the perspective of a "world without agriculture" which underpins the economic paradigm of "structural transformation" and "modern growth". It does so by recomposing worldwide land and labour productivity trends in caloric terms from 1961 to 2007 and by providing an heuristic model showing that the "Lewis Path" to prosperity is only one out of four possible pathways. It shows that more than half of the world population is rather embarked in a "Lewis Trap" where farmers are increasingly numerous and relatively poorer. It highlights how land scarcity and insufficient job opportunities outside agriculture prevent them to increase their labour productivity and incomes with motorized machineries. The emerging paradigm of "ecological intensification" might contribute to overcome the current deadlocks by redirecting worldwide R&D towards small-scale knowledge-intensive and context-specific agricultures overlapping the manufacture and service sectors. (Résumé d'auteur