Double Wronskian Soliton Solution for Mixed AKNS System

The Lax pair of the mixed Ablowitz--Kap--Newell--Segur (AKNS) system is obtained from compatibility condition. Hirota’s bilinear form is derived by some dependent variable transformation. Moreover, by means of the Wronskian technique, the double Wronskian form of soliton solutions are found. Specially, the two-soliton solution is presented.