Nonlocal integrable equations from the constrained BKP hierarchy

In this paper, first we construct a nonlocal integrable hierarchy, called the constrained nonlocal BKP hierarchy, which is a generalization of the intermediate long wave hierarchy. Second, we construct the corresponding bilinear equations. Third, we construct a tau function to solve the Hirota bilinear equations of the constrained nonlocal BKP hierarchy using neutral free fermions. Finally, we construct the rational solutions of the constrained nonlocal BKP hierarchy.