Nonlocal symmetries and exact solutions of variable coefficient AKNS system

TL;DR

This paper explores nonlocal symmetries of the variable coefficient AKNS system, localizes them to Lie point symmetries, and derives explicit solutions demonstrating their dynamic behavior.

Contribution

It introduces the first analysis of nonlocal symmetries for the variable coefficient AKNS system and localizes them to find explicit solutions.

Findings

Derived nonlocal symmetries using the lax pair.

Localized nonlocal symmetries to Lie point symmetries.

Obtained explicit analytic solutions and visualized their dynamics.

Abstract

In this paper, nonlocal symmetries of variable coefficient Ablowitz-Kaup-Newell-Segur(AKNS) system are discussed for the first time. With lax pair of time-dependent coefficient AKNS system, the nonlocal symmetries are obtained, and they are successfully localized to a Lie point symmetries by introducing a suitable auxiliary dependent variable. Furthermore, using the obtained Lie point symmetries of closed system, we give out two types of symmetry reduction and explicit analytic solutions. For some interesting solutions, the figures are given out to show their dynamic behavior.