Soliton Solutions, Breathers And Rogue Waves Of Several Nonlinear Integrable Systems

The soliton theory plays a significant role in the nonlinear science. The develop-ment of the soliton theory which has become main instrument to solve nonlinear partial differential equations, has opened up a new direction for the study of nonlinear science. Specially, some nonlinear models involved in the fluid mechanics, the nonlinear optics, the plasma physics and other fields of natural science, can be described by the soliton equations. This paper mainly gains the solutions of three different nonlinear integrable systems based on Darboux transformation method, including classical complex mKdV system, coherently coupled nonlinear Schrodinger system and AB system.The arrangements of the paper as follows:In the first chapter, the research and development of the soliton theory in recent years are introduced at first. Then, we explain the specific content of the Painleve integrable property and the Darboux transformation method. Finally, the whole work of this thesis was summarized.In the second chapter, the Painleve integrable property of the classical complex mKdV system are investigated. Via the Darboux transformation method, one-and two-breathers, localized solutions and parallel breathers are presented on the continuous wave background. Then, the propagation characteristics of those solutions will be analyzed by some figures plotted.In the third chapter, under analysis is coherently coupled nonlinear Schrodinger system which describes the propagation of polarized optical waves in an isotropic medi-um. By virtue of the Darboux transformation, some solutions have been generated on the vanishing and non-vanishing background, including solitons, breathers, bound solutions and first-order rogue waves. Dynamic behaviors of those solutions have been discussed through graphic simulation.In the fourth chapter, the conservation law of the AB system is discussed. Based on the Darboux transformation, one-and two-solitons and bound solitons have been obtained. At the same time, figures of the solutions are plotted.In the fifth chapter, the conclusions and the prospects about the research content are addressed.