Riemann–Hilbert problems of a nonlocal reverse-time six-component AKNS system of fourth order and its exact soliton solutions

We investigate the solvability of an integrable nonlinear nonlocal reverse-time six-component fourth-order AKNS system generated from a reduced coupled AKNS hierarchy under a reverse-time reduction. Riemann–Hilbert problems will be formulated by using the associated matrix spectral problems, and exact soliton solutions will be derived from the reflectionless case corresponding to an identity jump matrix.

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.

Symmetry Analysis, Bäcklund Transformations, and Interaction Solutions for an AB Modified KdV System

An AB modified KdV (AB-mKdV) system which can be used to describe two-place event is studied in this manuscript. Because the AB-mKdV system is considered as a special reduction of the famous AKNS system, the properties of the AKNS system are first revealed by using symmetry analysis. The nonlocal symmetries related to truncated Painlevé expansion, the finite transformation, and the symmetry reduction solutions of the AKNS system are presented. The corresponding Bäcklund transformations and the interaction solutions of the AB-mKdV system are constructed based on the special reduction. The results demonstrate that the AB-mKdV system possesses many kinds of interaction solutions, such as the interactions between kink and soliton and kink and cnoidal waves. The soliton can be changed from bright to dark during propagation.