Integrable decomposition for the (2+1)-dimensional AKNS hierarchy and its applications

In this paper, we are concerned with the integrable decomposition for (2+1)-dimensional Ablowitz–Kaup–Newell–Segur (AKNS) hierarchy. By utilizing recursive relations and symmetric reductions, propose that (n2 − n1 + 1)-flow of AKNS hierarchy can be decomposed into corresponding n1-flow n2-flow (1+1)-dimensional hierarchy, both in coupled reduced cases. As an appropriate generalization, decompositions standard Heisenberg ferromagnet equation, modified their two generalizations investigated. With no loss generality, one-soliton solutions dynamic projections relevant gauge equivalent structures discussed illustrated through some figures.