Solutions and connections of nonlocal derivative nonlinear Schrödinger equations
- 20 Downloads
All possible nonlocal versions of the derivative nonlinear Schrödinger equations are derived by the nonlocal reduction from the Chen–Lee–Liu equation, the Kaup–Newell equation and the Gerdjikov–Ivanov equation which are gauge equivalent to each other. Their solutions are obtained by composing constraint conditions on the double Wronskian solution of the Chen–Lee–Liu equation and the nonlocal analogues of the gauge transformations among them. Through the Jordan decomposition theorem, those solutions of the reduced equations from the Chen–Lee–Liu equation can be written as canonical form within real field.
KeywordsNonlocal derivative nonlinear Schrödinger equations Nonlocal reduction Double Wronskian Canonical form
This work is supported by the National Natural Science Foundation of China (NSFC) grant (Grant Number 11501510) and the Natural Science Foundation of Zhejiang Province (No. LY17A010024).
Compliance with ethical standards
Conflict of interest
The authors declare that there is no conflict of interests regarding the publication of this paper.
- 10.Zhou, Z.X.: Darboux transformations and global explicit solutions for nonlocal Davey–Stewartson I equation, arXiv:1612.05689 (2016)
- 14.Yang, J.K,: General N-solitons and their dynamics in several nonlocal nonlinear Schrödinger equation, arXiv:1712.01181 [nlin.SI] (2017)
- 15.Feng, B.F., Luo, X.D., Ablowitz, M.J., Musslimani, Z.H.: Genenral soliton solutions to a nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions, arXiv:1712.09172 (2017)
- 18.Shi, Y., Zhang, Y.S., Xu, S.W.: Families of nonsingular soliton solutions of a nonlocal Schrödinger-Boussinesq equation. Nonlinear Dyn. https://doi.org/10.1007/s11071-018-4491-8