Nonlocal symmetries and exact solutions of variable coefficient AKNS system

2018/05/10 by Xiangpeng Xin, Xin, Xiangpeng, Hanze Liu +3 · 1 citation
Physics and Astronomy · Chemistry · #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Molecular spectroscopy and chirality

paper · pdf · doi:10.48550/arxiv.1805.03878

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.

Cited by

• Symmetry analysis and new partially invariant solutions for the gas dynamics system with a special equation of state

Related

• High order nonlocal symmetries and exact solutions of variable coefficient KdV equation
• Nonlocal symmetries of systems of evolution equations
• Some comments on continuous symmetries of AKNS hierarchy equations and their solutions
• Solutions of local and nonlocal equations reduced from the AKNS hierarchy
• Solutions of Nonlocal Equations Reduced from the AKNS Hierarchy