Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger equation

•An extended generalized Darboux transformation method is proposed.•Three types of hybrid rogue wave and breather solutions are obtained for a classical nonlinear Schrodinger equation.•The control and interaction of the hybrid wave solution are graphically demonstrated.•An exact link is established...

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Published in:Applied mathematics and computation Vol. 386; p. 125469
Main Authors: Li, Bang-Qing, Ma, Yu-Lan
Format: Journal Article
Language:English
Published: Elsevier Inc 01.12.2020
Subjects:
Breather
Extended generalized Darboux transformation
Hybrid wave solution
Nonlinear Schrödinger system
Rogue wave
Extended generalized Darboux transformation
Nonlinear Schrödinger system
Breather
Rogue wave
Hybrid wave solution
ISSN:0096-3003
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Abstract •An extended generalized Darboux transformation method is proposed.•Three types of hybrid rogue wave and breather solutions are obtained for a classical nonlinear Schrodinger equation.•The control and interaction of the hybrid wave solution are graphically demonstrated.•An exact link is established between the hybrid solutions and the rogue wave solutions. An extended generalized Darboux transformation method is proposed to construct the hybrid rogue wave and breather solutions for a classical nonlinear Schrödinger equation. Three types of hybrid wave solutions are obtained: (i) the hybrid first-order rogue wave and breather; (ii) the hybrid second-order rogue wave and first-order breather; (iii) the hybrid first-order rogue wave and second-order breather. These solutions are novel and can be used to investigate the dynamical characteristic of the hybrid rogue waves and breathers. The control and interaction based on the parameters of the hybrid wave solution are graphically demonstrated. An exact link is established between the hybrid solutions and the rogue wave solutions via setting the parameter at special value.
AbstractList •An extended generalized Darboux transformation method is proposed.•Three types of hybrid rogue wave and breather solutions are obtained for a classical nonlinear Schrodinger equation.•The control and interaction of the hybrid wave solution are graphically demonstrated.•An exact link is established between the hybrid solutions and the rogue wave solutions. An extended generalized Darboux transformation method is proposed to construct the hybrid rogue wave and breather solutions for a classical nonlinear Schrödinger equation. Three types of hybrid wave solutions are obtained: (i) the hybrid first-order rogue wave and breather; (ii) the hybrid second-order rogue wave and first-order breather; (iii) the hybrid first-order rogue wave and second-order breather. These solutions are novel and can be used to investigate the dynamical characteristic of the hybrid rogue waves and breathers. The control and interaction based on the parameters of the hybrid wave solution are graphically demonstrated. An exact link is established between the hybrid solutions and the rogue wave solutions via setting the parameter at special value.
ArticleNumber 125469
Author Ma, Yu-Lan
Li, Bang-Qing
Author_xml – sequence: 1
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  surname: Li
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– sequence: 2
  givenname: Yu-Lan
  surname: Ma
  fullname: Ma, Yu-Lan
  email: mayl@th.btbu.edu.cn
  organization: School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, PR China
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Keywords Extended generalized Darboux transformation
Nonlinear Schrödinger system
Breather
Rogue wave
Hybrid wave solution
Language English
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Snippet •An extended generalized Darboux transformation method is proposed.•Three types of hybrid rogue wave and breather solutions are obtained for a classical...
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StartPage 125469
SubjectTerms Breather
Extended generalized Darboux transformation
Hybrid wave solution
Nonlinear Schrödinger system
Rogue wave
Title Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger equation
URI https://dx.doi.org/10.1016/j.amc.2020.125469
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