A Note on the Bilinearization of the Generalized Derivative Nonlinear Schrödinger Equation

The bilinearization of the generalized derivative nonlinear Schrödinger (GDNLS) equation is investigated systematically. It is known recently that the GDNLS equation can be decomposed into two different bilinear systems under the vanishing and nonvanishing boundary condition, respectively. However, it remains a question of how these two systems are related. In this letter, we show that all the bilinear equations can be derived uniformly from the KP hierarchy through appropriate reductions. Bright and dark soliton solutions in terms of Gram-type determinants are presented.