The breather, breather-positon, rogue wave for the reverse space-time nonlocal short pulse equation in nonzero background

In this paper, by using the Darboux transformation (DT), two types of breather solutions for the reverse space-time (RST) nonlocal short pulse equation are constructed in nonzero background: bounded and unbounded breather solutions. The degenerate DT is obtained by taking the limit of eigenvalues and performing a higher-order Taylor expansion. Then the N order breather-positon solutions are generated through degenerate DT. Some properties of the breather-positon solutions are discussed. Furthermore, rogue wave solutions are derived through the degeneration of breather-positon solutions.