Darboux Transformation and Multi-Solitons for Complex mKdV Equation

An explicit N-fold Darboux transformation with multi-parameters for coupled mKdV equation is constructed with the help of a gauge transformation of the
Ablowitz--Kaup--Newell--Segur (AKNS) system spectral problem. By using the Darboux transformation and the reduction technique, some multi-soliton solutions for the complex mKdV equation are obtained.