Two soliton interaction of Zakharov–Mikhailov spinor models

Abstract

We outline the spectral properties of their Lax operators for the Zakharov-Mikhailov spinor model (ZMm) and construct their fundamental analytic solutions (FAS). Using the dressing Zakahrov-Shabat method we derive the dressing factors for the one-soliton u 1(z 1, Φ1) and u 2(z 1 , z 2, Φ1, Φ2) for the two-soliton solutions. Next we calculate the asymptotics of the dressing factors of u 1(z 1, Φ1) for z 1 → ±∞. Inserting them into u 2(z 1 , z 2, Φ1, Φ2) we find that for z 1 → ±∞ u 2(z 1 , z 2, Φ1, Φ2) goes into one-soliton solutions but with shifted center of mass and shifted phase. Thus we conclude that the 2-soliton interactions of ZMm are purely elastic and are characterized by the above mentioned shifts.