Soliton solutions of weakly bound states for higher-order Ito equation

By utilizing an ingenious limit method proposed in this paper, the soliton solutions of weakly bound state including the multiple-pole solutions and the degenerate solution of breather solutions can be derived from the N-soliton solutions for higher-order Ito equation. By improving the traditional limit method, the dark double-pole solution can be obtained. Furthermore, some general forms of the multiple-pole solutions including the triple-pole solutions, quadruple-pole solutions, penta-pole solutions and the degenerate solution of breather solutions are derived. In addition, some dynamic behaviors of multiple-pole solutions are also specifically proposed. This limit method can also be applied to other integrable systems.