Two-breather solutions for the class I infinitely extended nonlinear Schrödinger equation and their special cases

  • M. CrabbEmail author
  • N. Akhmediev
Original paper


We derive the two-breather solution of the class I infinitely extended nonlinear Schrödinger equation. We present a general form of this multi-parameter solution that includes infinitely many free parameters of the equation and free parameters of the two breather components. Particular cases of this solution include rogue wave triplets, and special cases of ‘breather-to-soliton’ and ‘rogue wave-to-soliton’ transformations. The presence of many parameters in the solution allows one to describe wave propagation problems with higher accuracy than with the use of the basic NLSE.


Infinitely extended NLSE Breathers Rogue waves 



The authors gratefully acknowledge the support of the Australian Research Council (Discovery Project DP150102057).

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. 2019

Authors and Affiliations

  1. 1.Optical Sciences Group, Research School of Physics and EngineeringThe Australian National UniversityCanberraAustralia

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