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Bilinear approach to supersymmetric AKNS system; multiple dressing of fermionic amplitudes

In this paper, we investigate the super-bilinear formalism and interaction of supersoliton solutions for the supersymmetric AKNS system [H. Aratyn and A. Das, Mod. Phys. Lett. A 13, 1185 (1998)]. It is shown that the super-bilinear form involves an auxiliary fermionic tau function and the supersolitons have less freedom than expected (concerning the dependence on fermionic parameters). Also, the interaction between super-solitons is much more complicated than in the case of real supersymmetric equations (KdV, mKdV, Sawada–Kotera, Sine–Gordon, etc.), involving four types of dressing of the fermionic parameters. These solutions are general compared to the ones found in Ref. 1 which contain no fermionic parameter.