In this paper, the first and N -th Darboux transformation for the integrable Kuralay-IIA equation are constructed by using the gauge transformation and the reduction condition associated with the integrability, from which various nonlinear wave solutions can be obtained. Specifically, the first and second breather waves are derived by selecting different parameters, whose nonlinear dynamics have also been discussed. The findings indicate that the real and imaginary parts of the breather waves can exhibit the characteristics of breather waves on the periodic wave backgrounds. The relevant results are expected to reveal the theoretical mechanism of nonlinear phenomena in fields such as magnetism and so on.
Liu et al. (Sun,) studied this question.