Riemann–Hilbert problem and [formula omitted]-soliton solutions for the [formula omitted]-component derivative nonlinear Schrödinger equations

Abstract

The n-component derivative nonlinear Schrödinger (DNLS) equations are discussed by the Riemann–Hilbert approach. By developing an improved Riemann–Hilbert problem, explicit soliton solutions of the n-component DNLS equations are obtained. Different from soliton solutions in many literatures, our expression does not include unfriendly integrals. An invariant and its general formula of the single-soliton solution for any n-component DNLS equations are derived. For the 2-component DNLS equation, we obtain one type of interesting solution — double hump soliton. The results play important roles in the vector solitons in many nonlinear physical systems, such as Bose–Einstein condensates, nonlinear optical fibers, etc.