Studies on integrability of some perturbed nonlinear evolution equations

Usually typical dynamical systems are non integrable. But few systems of practical interest are integrable. The soliton concept is a sophisticated mathematical construct based on the integrability of a class ol' nonlinear differential equations. An important feature in the clevelopment. of the theory of solitons and of complete integrability has been the interplay between mathematics and physics. Every integrable system has a lo11g list of special properties that hold for integrable equations and only for them. Actually there is no specific definition for integrability that is suitable for all cases. .There exist several integrable partial clillerential equations( pdes) which can be derived using physically meaningful asymptotic teclmiques from a very large class of pdes. It has been established that many 110nlinear wa.ve equations have solutions of the soliton type and the theory of solitons has found applications in many areas of science. Among these, well-known equations are Korteweg de-Vries(KdV), modified KclV, Nonlinear Schr6dinger(NLS), sine Gordon(SG) etc..These are completely integrable systems. Since a small change in the governing nonlinear prle may cause the destruction of the integrability of the system, it is interesting to study the effect of small perturbations in these equations. This is the motivation of the present work.

A study of the evolution and working of regulated markets in Tamilnadu

This study presents a detailed investigation of the origin and development of regulations in agricultural marketing in Tamil Nadu. It evaluates the method and process of regulation practised through the orgahisation of a chain of regulated markets in the State. The study also examines in detail the conceptual frame work behind state intervention and show the original concept has been modified subsequently to suit the changed conditions during the post-independence era of planning for economic development Specific objectives explained in the present study include the following: viz, a) The historical aspects that necessitated state intervention in agricultural marketing in the form of organising regulated markets and their evolution, b) The conceptual and organisational bases of regulated markets in Tamil Nadu. c) The impact of such regulations on the existing trade channels or systems.168 d) The performance and efficiency of regulated markets and their achievements. The study also has suggested some remedial measures to reorganise the present organisational pattern of regulated marketing in Tamil Nadu.