The dynamic of the positons for the reverse space–time nonlocal short pulse equation

Abstract

In this paper, the Darboux transformation (DT) of the reverse space–time (RST) nonlocal short pulse equation is constructed by a hodograph transformation and the eigenfunctions of its Lax pair. The multi-soliton solutions of the RST nonlocal short pulse equation are produced through the DT, which can be expressed in terms of determinant representation. The correctness of DT and determinant representation of N-soliton solutions are proven. By taking different values of eigenvalues, bounded soliton solutions and unbounded soliton solutions can be obtained. In addition, based on the degenerate Darboux transformation, the $N$-positon solutions of the RST nonlocal short pulse equation are computed from the determinant expression of the multi-soliton solution. The decomposition of positons, approximate trajectory and “phase shift” after collision are discussed explicitly. Furthermore, different kinds of mixed solutions are also presented, and the interaction properties between positons and solitons are investigated.