Higher-order Soliton Solutions To The Gerdjikov-ivanov Equation By The Dressing Method

Getting the soliton solutions to the nonlinear soliton equations is one of theimportant tasks in the theory of the integrable systems. In general, the solitonsolutions obtained are the ones associated with simple poles, while the studies aboutthe higher-order soliton solutions are rare. In this paper, we shall study the Gerdjikov–Ivanov equation by the dressing method, and derive its one-order soliton solutionand two-order soliton solution. We consider that the dressing factor have the simplepoles and the poles of order2, respectively. After the dressing transformation for theeigenfunction associated with the seed solution, we discussed the regularizationconditions about the dressed eigenfunctions, and then established the relationshipbetween the potential and the scattering data. In this way, the simple N-solitonsolution and the2-order soliton solution of the Gerdjikov–Ivanov equation areobtained.