Solutions of the nonlocal (2+1)-D breaking solitons hierarchy and the negative order AKNS hierarchy

Abstract The (2+1)-dimensional nonlocal breaking solitons AKNS hierarchy and the nonlocal negative order AKNS hierarchy are presented. Solutions in double Wronskian form of these two hierarchies are derived by means of a reduction technique from those of the unreduced hierarchies. The advantage of our method is that we start from the known solutions of the unreduced bilinear equations, and obtain solitons and multiple-pole solutions for the variety of classical and nonlocal reductions. Dynamical behaviors of some obtained solutions are illustrated. It is remarkable that for some real nonlocal equations, amplitudes of solutions are related to the independent variables that are reversed in the real nonlocal reductions.