Some non- linear problems in theoretical physics

An immense variety of problems in theoretical physics are of the non-linear type. Non~linear partial differential equations (NPDE) have almost become the rule rather than an exception in diverse branches of physics such as fluid mechanics, field theory, particle physics, statistical physics and optics, and the construction of exact solutions of these equations constitutes one of the most vigorous activities in theoretical physics today. The thesis entitled ‘Some Non-linear Problems in Theoretical Physics’ addresses various aspects of this problem at the classical level. For obtaining exact solutions we have used mathematical tools like the bilinear operator method, base equation technique and similarity method with emphasis on its group theoretical aspects. The thesis deals with certain methods of finding exact solutions of a number of non-linear partial differential equations of importance to theoretical physics. Some of these new solutions are of relevance from the applications point of view in diverse branches such as elementary particle physics, field theory, solid state physics and non-linear optics and give some insight into the stable or unstable behavior of dynamical Systems The thesis consists of six chapters.

Studies On Some Aspects Of Phytoplankton

The present study is concentrated on a composite group of algae of phy— toplankton. The algae in the aquatic environment are the most important of all ch1orophy1l- bearing life on earth on which considerable attention is being given on account of their supreme status in the aquatic food chain. Though the higher plants serve as the major primary producers in the terrestrial biocycle, the primary producers in the aquatic ecosystem especially in the marine environment-" assume unparalleled significance ‘because of their c'ontribution.to the high magnitude of production generating the fishery resources