Frontiers in Physics (Mar 2023)

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

  • Xinrui Shi,
  • Xinrui Shi,
  • Yunqing Yang,
  • Yunqing Yang

DOI
https://doi.org/10.3389/fphy.2023.1179961
Journal volume & issue
Vol. 11

Abstract

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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.

Keywords