The Dressing Method and Dynamics of soliton solutions for the Kundu-Eckhaus equation

Abstract The boundary value problem for focusing Kundu-Eckhaus equation with non-zero boundary conditions is studied by the Dbar dressing method in this work. A Dbar problem with non-canonical normalization condition is introduced to investigate the soliton solution. The eigenfunction of Dbar problem is meromorphic outside annulus with center 0, which is used to construct the Lax pair of the Kundu-Eckhaus equation with non-zero boundary conditions, which is a crucial step to further search for the soliton solution. Furthermore, the original nonlinear evolution equation and conservation law are obtained by means of choosing a special distribution matrix. Moreover, the N -soliton solutions of focusing Kundu-Eckhaus equation with non-zero boundary conditions are discussed based on the symmetries and distribution. As concrete examples, the dynamic behaviors of the one-breather solution and the two-breather solution are analyzed graphically by considering different parameters.PACS 05.45.Yv, 03.75.Lm, 42.65.Tg