Riemann-Hilbert approach and N-soliton formula for coupled derivative Schrödinger equation

The coupled derivative Schrödinger equation is studied in the framework of the Riemann-Hilbert problem and a compact N-soliton solution formula is found. Taking advantage of this result, some properties for single soliton solution and asymptotic analysis of N-soliton solution are explored. As a by-product, a coupled Fokas-Lenells equation together its N-soliton solution is presented.