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

TL;DR

This paper constructs Darboux transformations for the reverse space-time nonlocal short pulse equation, deriving multi-soliton, positon, and mixed solutions, and analyzing their interactions.

Contribution

It introduces a novel Darboux transformation approach for the RST nonlocal short pulse equation and derives explicit multi-soliton and positon solutions with interaction analysis.

Findings

Explicit multi-soliton solutions expressed via determinants.

Bounded and unbounded soliton solutions obtained by varying eigenvalues.

Interaction properties between positons and solitons analyzed.

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. 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. Furthermore, different kinds of mixed solutions are also presented, and the interaction properties between positons and solitons are investigated.