Study Of Nonlinear Waves In Dusty Plasmas

In resent years, the dusty plasmas become a rapidly growing research domain, thus, it is important to do research on the dusty plasmas and its physical qualities in many other domain, such as space detection, laboratory and industrial processing and so on. There is also some referenced values for newly cross subject. This thesis not only base on the importance of the dusty plasmas research but also combine the corresponding knowledge in nonlinear science domain, in order to analyze the theoretical models in dusty plasmas and obtain some useful theoretical results which can verify the observational results and experimental results. This thesis is organized as follows:In chapter 1, the conception, origin, character and current research situation are introduced. Three basic means widely used by many researchers are simply introduced, that is, theoretical analysis, numerical simulation and experimental research. In chapter 2, firstly, various nonlinear waves and nonlinear structures as well as their developing history are introduced. Then two methods in theoretical analysis-reductive perturbation method and Sagdeev potential method will be introduced and their merits and defects are also respectively pointed out. Finally, various methods, which are used to obtain the analytical solutions of the nonlinear equations governing the nonlinear waves, are introduced in great detail. We mainly introduce three methods, that is, extended hyperbolic function method, generalized projected Ricatti equation expansion method and the Tanh-function method which based on the extended projective method. We will illustrate these methods by specific examples.Nowadays both theoretical and experimental investigations have extended the concept of solitons to include the cylindrically and spherically expanding or contracting nonlinear waves displaying general soliton properties with the exception that their amplitudes are functions of the radial distance. However, the transverse perturbations are still neglected by many authors, in fact, the inevitable existence of transverse perturbations will change the solitonary structure a lot. Thus, we should consider the effect of the transverse perturbations. In addition, it is important to notice that, in laboratory and space plasmas, negatively charged dust fluid and ions of two different temperatures (cold and hot) are the major plasma species and should be considered in the models. In chapter 3, the cylindrical Kadomstev-Petviashvili(KP) equation, which is a...