Breather,Rogue Wave Solutions And Breather-to-soliton Conversions For Two Types Of(2+1)-dimensional Soliton Equations

In this paper,we mainly study two kinds of(2+1)-dimensional soliton equations,which are(2+1)-dimensional nonlinear Schr(?)dinger-Maxwell-Bloch(NLS-MB)equations and the(2+1)-dimensional complex modified KdV-Maxwell-Bloch(cmKdV-MB)equations.Based on the plane wave solutions,two types of breather solutions(Kuznetsov-Ma breather and Akhmediev breather),rogue wave solutions and breather-to-soliton conversions are derived by using the Darboux transformation(DT)method.The traveling wave state and characteristics of solutions can be discussed by adjusting the parameters.Firstly,we study the(2+1)-dimensional NLS-MB equations and construct the N-fold generalized DT through its Lax pair.And we obtain two different kinds of breather solutions,rogue wave solutions and breather-to-soliton conversions under the background of initial non-zero solutions.At the same time,we describe the image of the solutions by adjusting and controlling the parameters,and analyze the dynamic change characteristics of the solutions through the graph.Secondly,we investigate the(2+1)-dimensional cmKdV-MB equations.Starting from the Lax pair of the equation,the N-fold generalized DT is expressed in determinant form.Based on the DT obtained,we can get breather solutions,rogue wave solutions and breather-to-soliton conversions in the plane wave background.And the Mathematica is used to simulate graphs and explore the transmission characteristics of the solutions.