The Solutions And Application Of The(2+1)-Demonsional Davey-Stewartson-Like Equations In Dusty Plasmas

Plasma physics is a new branch of science founded on many classical physical theories which explores the shape and collective movements of plasmas, as well as its interaction with electromotive force(EMF) and other substance. Soliton phenomenon, a coherent structure appears in much of the nonlinear field. As a complicated nonlinear system, plasmas provide a quite suitable platform for soliton research. What’s more, soliton research on plasma plays an important role in instability of plasma system, space exploration, solar-terrestrial space, energy transportation of waves and particles among different parts of magnetospheres, and fields like experiments and industries.Considering the importance of dusty plasma research, we analyze models in different dusty plasmas with non-linear science, especially relative soliton theories, and then search for the solitary wave in these system models. We mainly explore stability of solitary wave and interactive dynamics among them by discussing characters of soliton waves in dusty solitons and dusty sound waves from a nonlinear dynamic perspective. The contents of this paper are as follow:Chapter1introduces the background, main tasks and conclusions of our research.In chapter2, we first make a brief introduction of the origin, definition and characteristics of dusty plasma. Then we move on to non-linear soliton waves in plasmas, including soliton waves of high or low frequency in plasma and soliton waves in dusty plasma. Finally, we introduce two research methods which are frequently used by researchers--Reduetive Perturbation method and Pseudopotential method, and then made a comparison on their advantages and applicable conditions.Chapter3further introduces soliton solutions of non-linear equations, with a focus on Bell polynomials and Hirota method.The next three chapters goes further with three sets of equations:(2+1)-dimensional variable coefficient Davey-Stewartson-like (DS) equation,(3+1)-dimensional general DS-like equation and fifth order (2+1) general Sawada-Kotera (SK) equation, which are all applied in dusty plasma.These three sets of equations compose a set of DS-like equation in a progressively increasing manner in dimensions and orders. We systematically consider these equations with non-linear solutions.First of all, we get the three sets of equations from physics systems with Reduetive Perturbation method.Then we modulate dust acoustic wave to the disturbed small amplitude. Considering different scale transformation, we get the DS equation describing unmagnetized DAW with small amplitude. This equation, which is integrable and has a constant coefficients version and a variable coefficients version, is a two dimensional extension of one dimension NLS equation.If we consider lateral disturbance from two directions, we can get a three dimension DS equation in the same way.For unmagnetized plasmas, the extension of DS equation from (2+1) dimension to (3+1) dimension won’t bring any physical implications, thus we focus on (2+1) dimension DS equation.Meanwhile, to get DS equation from high order general SK equation, we can use approximate Fourier Transform. With the same method, we can analyze five order (2+1) dimension SK equation, find the soliton solution and analyze characteristics of soliton waves via charters.The last chapter is the summery and prospects.