A $$\overline{\partial }$$-dressing method for the mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation

Abstract In this work, we apply the $$\overline{\partial }$$ ∂ ¯ -dressing method to study mixed Chen–Lee–Liu derivative nonlinear Schrödinger equation (CLL–NLS) with non-normalization boundary conditions. The spatial and time spectral problems associate CLL–NLS which are derived from local $$2 \times 2$$ 2 × matrix. A hierachy source is proposed by using recursive operator. Based on -equation, N-solitons of constructed choosing a special transformation Further more, explicit two-soliton obtained.