Novel higher-order rational solitons and dynamics of the defocusing integrable nonlocal nonlinear Schrödinger equation via the determinants

We investigate the defocusing integrable nonlocal nonlinear Schrödinger (nNLS) equation using the loop group method and perturbation expansion idea. The associated N-fold Darboux transformation is presented in terms of the simple determinants. As the application of the N-fold Darboux transformation, we find the higher-order rational solitons of the nNLS equation, which exhibit many new types of soliton structures. Moreover, we also numerically study the stability of some rational solitons. The results are useful to explain the corresponding wave phenomena in nonlocal wave models.