Darboux Transformations And New Solutions For Two Types Of (2+1)-dimensional Soliton Equations

In this paper,we investigate two types of(2+1)-dimensional soliton equations includ-ing the(2+1)-dimensional nonlinear Schrodinger-Maxwell-Bloch(NLS-MB)equations and the(2+1)-dimensional complex modified KdV-Maxwell-Bloch(cmKdV-MB)equations.By using the Darboux transformation(DT)method,two different kinds of soliton solutions(multi-line soliton and multi-parabola soliton solutions)are derived on the vanishing background.For the obtained soliton solutions,we discuss the processes and properties of their interactions through regulating parameters.The structure of the full thesis is arranged as follows:In chapter one,we present the development process of the soliton theory in nonlinear science,and then the basic idea of DT method is expounded.Finally,the main works and arrangements of this thesis are summarized.In chapter two,we investigate the(2+1)-dimensional NLS-MB equations.Based on the Lax pair,the two-fold DT is constructed for this equation.And we get two different kinds of soliton solutions at the zero seed.At the same time,we take potential function q as an example to carry out limit analysis.Finally,using Mathematica software to depict the graphics of the solutions,so the dynamic characteristics of the traveling wave of the soliton solutions are further analyzed.In chapter three,we investigate the(2+1)-dimensional cmKdV-MB equations.Accord-ing to the relevant Lax pair,the one-fold,N-fold DT are constructed by the determinant representation,and prove the results in detail.Then,by virtue of the DT constructed,the new soliton solutions of the equations under the initial zero solution can be obtained.Finally,figures of the solutions are plotted by adjusting different parameters,and the properties and characteristics of the solitons propagation are summarized.In chapter four,we summarize the conclusions of this thesis and point out the key points of future research.