Nonlinear Dynamics

, Volume 95, Issue 3, pp 1867–1877 | Cite as

Dynamics of some novel breather solutions and rogue waves for the PT-symmetric nonlocal soliton equations

  • Fajun YuEmail author
  • Li Li
Original Paper


A generalized nonlocal nonlinear Hirota (GNNH) equation with variable coefficients is presented, which can be reduced into the nonlocal Hirota equation with the self-induced PT-symmetric potential. Especially, the nonlocal Gross–Pitaevskii (NGP) equation with the self-induced PT-symmetric potential is derived from the GNNH equation. Then, we obtain some novel non-autonomous breather solutions and rogue waves of GNNH equation via similarity and Hirota methods, and consider some controllable behaviors of these non-autonomous wave solutions. Furthermore, some properties of the non-autonomous rational (NR) waves are investigated analytically for the NGP equation. The trajectories of peaks and depressions of the non-autonomous rogue waves are produced by means of analytical method, and the dynamical stabilities of the NR solution are derived through the numerical method. The obtained results are different from the solutions of the local nonlinear equations. Some different propagation phenomena can also be produced through manipulating non-autonomous rogue waves, which can present the potential applications for the rogue wave phenomena in nonlocal wave models.


Nonlocal Hirota equation Breather solution Rogue wave 



This work was sponsored by the Special Fund of Liaoning Provincial Universities’ Fundamental Scientific Research Projects, China (Grant No. LQN201711).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Mathematics and Systematic SciencesShenyang Normal UniversityShenyangChina

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