The Study Of PT Symmetric Optical Solitons Based On Mathematical Calculations

Soliton theory is an important branch of nonlinear dynamic system,which not only reflects a kind of very stable phenomenon in nature,but also provides theoretical guidance for the production practice of people,such as nonlinear optical fiber communications,fluid mechanics and other fields.At the same time,there are also many methods for solving nonlinear partial differential equations,such as Hirota direct method,Darboux transformation,Painlevé analysis and Inverse scattering method.The main content of this thesis is to solve the soliton solutions of nonlinear evolution equation based on mathematical calculation and discuss its dynamic characteristics.The specific content includes the following three parts:In the first part,the development history and research status of the PT symmetric spatial optical solitons are briefly described.The development of the PT symmetric spatial optical solitons,the development of computer mathematical calculation and several commonly used soliton-solving methods,such as Hirota direct method,Darboux transformation and Inverse scattering method are introduced.In the second part,through the study of the generalized high-order nonlinear Schr(?)dinger equation,we discuss the four equations derived from the nonlocal high order nonlinear Schr(?)dinger equation.The high order nonlinear Schr(?)dinger equation,the time symmetric nonlocal high order nonlinear Schr(?)dinger equation,the space symmetric nonlocal high order nonlinear Schr(?)dinger equation and the time and space symmetric nonlocal high order nonlinear Schr(?)dinger equation.Since many results have been obtained for the high order nonlinear Schr(?)dinger equation,the last three equations are discussed in this paper.By means of the Hirota bilinear method,the higher order analytical solutions of the generalized high order coupled nonlinear Schr(?)dinger equations are obtained.In the third part,the scalar Maxwell-Bloch equations are studied by using the Darboux transformation.The multisoliton solutions of integrable Maxwell-Bloch equations are obtained,and the propagation and interaction of solitons are analyzed:the effects of spectral parameters on the propagation direction of single solitons are analyzed;Different interaction modes of two and three solitons for Maxwell-Bloch equations are obtained by selecting different spectral parameters.