\({\overline \partial}\)-dressing Method for the Coupled Two-component Kundu-Eckhaus Equations

Abstract

In this paper, \({\overline \partial}\)-dressing method based on a local 3 × 3 matrix \({\overline \partial}\)-problem with non-normalization boundary conditions is used to investigate coupled two-component Kundu-Eckhaus equations. Firstly, we propose a new compatible system with singular dispersion relation, that is time spectral problem and spatial spectral problem of coupled two-component Kundu-Eckhaus equations via constraint equations. Then, we derive a hierarchy of nonlinear evolution equations by introducing a recursive operator. At last, by solving constraint matrixes, a spectral transform matrix is given which is sufficiently important for finding soliton solutions of potential function, and we obtain N-soliton solutions of coupled two-component Kundu-Eckhaus equations.