Double-Pole Solution and Soliton-Antisoliton Pair Solution of MNLSE/DNLSE Based upon Hirota Method

Hirota method is applied to solve the modified nonlinear Schrödinger equation/the derivative nonlinear Schrödinger equation (MNLSE/DNLSE) under nonvanishing boundary conditions (NVBC) and lead to a single and double-pole soliton solution in an explicit form. The general procedures of Hirota method are presented, as well as the limit approach of constructing a soliton-antisoliton pair of equal amplitude with a particular chirp. The evolution figures of these soliton solutions are displayed and analyzed. The influence of the perturbation term and background oscillation strength upon the DPS is also discussed.