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In the paper possible local and nonlocal reductions of theAblowitz-Kaup-Newell-Suger (AKNS) hierarchy are collected, including theKorteweg-de Vries (KdV) hierarchy, modified KdV hierarchy and their nonlocalversions, nonlinear Schr\"{o}dinger hierarchy and their nonlocal versions,sine-Gordon equation in nonpotential form and its nonlocal forms. A reductiontechnique for solutions is employed, by which exact solutions in doubleWronskian form are obtained for these reduced equations from those doubleWronskian solutions of the AKNS hierarchy. As examples of dynamics weillustrate new interaction of two-soliton solutions of the reverse-$t$nonlinear Schr\"{o}dinger equation. Although as a single soliton it is alwaysstationary, two solitons travel along completely symmetric trajectories in$\{x,t\}$ plane and their amplitudes are affected by phase parameters.Asymptotic analysis is given as demonstration. The approach and relationdescribed in this paper are systematic and general and can be used to othernonlocal equations.

Solutions of local and nonlocal equations reduced from the AKNS hierarchy