In this paper we provide a systematical bilinear approach to derive rational solutions (in terms of envelope | q |) living on a zero background and decaying algebraically for three derivative nonlinear Schrödinger equations, namely, the Kaup-Newell equation, the Chen-Lee-Liu equation and the Gerdjikov-Ivanov equation. We present a simpler unified bilinear form for these three equations. Their rational solutions with zero background are obtained in terms of double Wronskian via bilinear equations. Algebraic solitons resulting from rational solutions are presented. Asymptotic dynamics are analyzed and illustrated. Scattering of high order rational solutions are featured as waves with slowly varying amplitudes. Scattering of algebraic solitons behaves like usual solitons but asymptotically with zero phase shift.
PACS numbers: 02.30.Ik, 02.30.Ks, 05.45.Yv