Soliton And Rogue Wave Solution Of (2+1)-dimensional Derivative Nonlinear Schr?dinger Equation

In this paper,the main research content is focused on research the soliton and rogue wave solutions based on the theory of Darboux transformation for the?2+1?-dimensional derivative nonlinear Schrodinger equation,i.e.iq_t+q_xy±2i???_x[q???_x^-1???_y|q|²]=0.This equation is the important model in the theory of nonlinear PDE.The Lax pair of this equation is reviewed in detail.For obtaining the soliton and rogue solutions,a Darboux transformation is constructed in this paper.Here a_1.0,a_2.0,b_1.1,c_1.1 are decided by ? and Lax pair.The N-order Darboux transformation is successfully applied to the Lax pair and the general explicit formula for the N-soliton solution is derived in terms of determinanton the zero background.Two different kinds of soliton solutions?multi-line soliton andmulti-parabola soliton solutions?are constructed by applying the Darbouxtransformation.Also,the characteristics?propagation direction,wave vector and frequency?of two types of solitons are analyzed.The interactions are respectively displayed between line-solitons,between two parabola solitons,as well as between line-soliton with different direction and parabola-soliton based on the figures for several sample solutions.The N-order generalized Darboux transformation is derived,and the determinant form of N-order rogue waves is presented by taking limit on the classical Darboux transformation.Two different kinds of rogue wave solutions?linear rogue wave and parabolic rogue wave?are constructed successively on the plane wave solution background.The characteristics of two types of rogue waves are analyzed by some figures and physical qualities.