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

Abstract

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.