A ∂¯-dressing approach to the Kundu-Eckhaus equation

Abstract Starting from a local 2 × 2 matrix ∂ ¯ -equation with non-normalization boundary conditions, the spatial and time spectral problems associated with the Kundu-Eckhaus (KE) equation are derived via two linear constraint equations. The gauge equivalence among the KE equation, NLS equation and Heisenberg chain equation are given. A KE hierarchy with source is proposed by using recursive operator. The N-solitions of the KE equation are constructed based the ∂ ¯ -equation by choosing a special spectral transformation matrix. Further the explicit one- and two-soliton solutions are obtained.