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Nonlinear Dynamics

, Volume 92, Issue 3, pp 815–825 | Cite as

A general nonlocal nonlinear Schrödinger equation with shifted parity, charge-conjugate and delayed time reversal

  • Xiao-Yan Tang
  • Zu-Feng Liang
Original Paper

Abstract

A general nonlocal nonlinear Schrödinger equation with shifted parity, charge-conjugate and delayed time reversal is derived from the nonlinear inviscid dissipative and equivalent barotropic vorticity equation in a \(\beta \)-plane. The modulational instability (MI) of the obtained system is studied, which reveals a number of possibilities for the MI regions due to the generalized dispersion relation that relates the frequency and wavenumber of the modulating perturbations. Exact periodic solutions in terms of Jacobi elliptic functions are obtained, which, in the limit of the modulus approaches unity, reduce to soliton, kink solutions and their linear superpositions. Representative profiles of different nonlinear wave excitations are displayed graphically. These solutions can be used to model different blocking events in climate disasters. As an illustration, a special approximate solution is given to describe a kind of two correlated dipole blocking events.

Keywords

Nonlocal NLS equation Shifted parity Delayed time reversal Modulational instability Periodic waves 

Notes

Acknowledgements

The authors acknowledge the financial support by the National Natural Science Foundation of China (Nos. 11675055 and 11475052) and Shanghai Knowledge Service Platform for Trustworthy Internet of Things (No. ZF1213).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Shanghai Key Laboratory of Trustworthy ComputingEast China Normal UniversityShanghaiChina
  2. 2.Department of PhysicsHangzhou Normal UniversityHangzhouChina

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