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

M. Crabb; N. Akhmediev

doi:10.1007/s11071-019-05186-0

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

M. Crabb^*, N. Akhmediev

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	245-255
Number of pages	11
Journal	Nonlinear Dynamics
Volume	98
Issue number	1
DOIs	https://doi.org/10.1007/s11071-019-05186-0
Publication status	Published - 1 Oct 2019

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title = "Two-breather solutions for the class I infinitely extended nonlinear Schr{\"o}dinger equation and their special cases",

abstract = "We derive the two-breather solution of the class I infinitely extended nonlinear Schr{\"o}dinger 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 {\textquoteleft}breather-to-soliton{\textquoteright} and {\textquoteleft}rogue wave-to-soliton{\textquoteright} 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.",

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author = "M. Crabb and N. Akhmediev",

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AU - Akhmediev, N.

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N2 - 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.

AB - 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.

KW - Breathers

KW - Infinitely extended NLSE

KW - Rogue waves

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ER -

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

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