AUTHOR=Shi Xinrui , Yang Yunqing 

TITLE=Exact solutions and Darboux transformation for the reverse space–time non-local fifth-order non-linear Schrödinger equation

JOURNAL=Frontiers in Physics

VOLUME=11

YEAR=2023

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2023.1179961

DOI=10.3389/fphy.2023.1179961

ISSN=2296-424X

ABSTRACT=<p>In this paper, the non-local reverse space−time fifth-order non-linear Schrödinger(NLS) equation has been investigated, which is proposed by the non-local reduction of Ablowitz–Kaup–Newell–Segur (AKNS) scattering problems. The determinant representation of the Nth Darboux transformation for the non-local reverse space−time fifth-order NLS equation is obtained. Some interesting non-linear wave solutions, including soliton, complexiton, and rogue wave solutions, are derived by the Darboux transformation. Moreover, the dynamics of non-linear wave solutions are illustrated with the corresponding evolution plots, and the results show that the non-local fifth-order NLS equation has new different properties from the local case.</p>